# Show Root 2 Is A Irrational Number (2023)

Mathematics Middle School

Step-by-step explanation:

is irrational because it's decimal form has no pattern (never repeats) and it never terminates.

## Related Questions

Stefano accidentally dropped his sunglasses off the edge of a canyon as he was looking down. The height, h(t), in meters (as it relates to sea level), of the sunglasses after t seconds, is shown in the table. A 2-column table with 8 rows titled Height of Sunglasses Over Time. The first column is labeled t with entries 0, 1, 2, 3, 4, 5, 6, 7. The second column is labeled h(t) with entries 10, 5.1, negative 9.6, negative 34.1, negative 68.4, negative 112.5, negative 166.4, negative 230.1.

During its descent, the pair of sunglasses passed by a climber in the canyon 6 seconds after Stefano dropped them. To the nearest meter, what is difference in elevation between Stefano and the climber?

166 meters
176 meters
230 meters
240 meters

Stefano's movement on the canyon is an illustration of elevation.

The difference in elevation is (b) 176 meters

Using the table as a guide.

• At 6 seconds, the height of the sunglass is -166.4 meters
• At the starting point (when t = 0), the height of the sunglass is 10 meters

So, the difference between the heights is:

Evaluate

Remove absolute brackets

Approximate

Hence, the difference in elevation is (b) 176 meters

brainly.com/question/4184020

176 meters

Step-by-step explanation:

Stefano is at +10 elevation, the hiker is at -166.4

10 + 166.4 = 176.4 ≈ 176 meters

Stefano accidentally dropped his sunglasses off the edge of a canyon as he was looking down. The height, h(t), in meters (as it relates to sea level), of the sunglasses after t seconds, is shown in the table. A 2-column table with 8 rows titled Height of Sunglasses Over Time. The first column is labeled t with entries 0, 1, 2, 3, 4, 5, 6, 7. The second column is labeled h(t) with entries 10, 5.1, negative 9.6, negative 34.1, negative 68.4, negative 112.5, negative 166.4, negative 230.1.

During its descent, the pair of sunglasses passed by a climber in the canyon 6 seconds after Stefano dropped them. To the nearest meter, what is difference in elevation between Stefano and the climber?

166 meters
176 meters
230 meters
240 meters

176 meters

Stefano is at +10 elevation while the hiker is at -166.4 elevation. The difference would be 10 - (-166.4) = 10 + 166.4 = 176.4 or approximately 176 meters

B. 176 meters

Step-by-step explanation:

I took it on EDGE

AB has endpoints at A(4, -8) and B(-6, -2). What are the coordinates of the midpoint of AB?
O (1,-5)
O (2,10)
O (1,5)
(
2
10)
0 (-1,5)
0 (-2, 10)
0 (-2,-10)
( 1,-5)

The coordinates of the mid - point of the line AB is (-1, -5).

What is mid - point?

A midpoint is a point that divides a given line into two equal parts.

Given is that AB has endpoints at A(4, -8) and B(-6, -2). It is asked to find the coordinates of the midpoint of AB.

We can write the coordinates of the midpoint of AB as -

{x} = (x₁ + x₂)/2

{x} = (4 - 6)/2

{x} = - 2/2

{x} = -1

{y} = (y₁ + y₂)/2

{y} = (-8 - 2)/2

{y} = - 10/2

{y} = - 5

Therefore, the coordinates of the mid - point of the line AB is (-1, -5).

To solve more questions on mid-points, visit the link below-

brainly.com/question/17079522

#SPJ7

Step-by-step explanation:

(-1;-5)

(Video) Proof that square root of 2 is irrational | Algebra I | Khan Academy

Use the diagram to answer the question. B(3,1)
C(13, 1)
A(3,-9)
© 2019 Strong Mind. Created using GeoGebra.
Which information about the coordinates of G and H will prove that GH is a median of AABC?
O G(-4, 3); H (1,8)
O G6,-8); H(16,8)
OG(3,-4); H(8,1)
G(1.5,5); H(8,5)

The first one is correct

Step-by-step explanation:

Point B is at (3,1). For which segment is B a midpoint?
O AC with endpoints at A(1,-1) and C(5,3)
O AD with endpoints at A(1,-1) and C(6,4)
O AC with endpoints at A(1,-1) and C(8,6)
AC with endpoints at A(1, -1) and C(7,5)

AC with end points A (1,-1) and C (5,3)

Step-by-step explanation:

mid point is calculated using the equation

so from AC, with end points A (1,-1) and C (5,3). If we substitute the values back into the equation.

When we solve we get the same values for the midpoint

sorry I couldn't get Commas so I used dots

Please find x 12x-3=3​

You would have to add 3 to both sides and then divide both sides by 12. your answer would be 1/2.

Answer: x = 2

Make -3 into a positive 3 and move it to the right.

3 + 3 = 6

12x/12= x

12/6 = 2

(Video) Proof: Square Root of 2 is Irrational

x = 6

If you still don’t get it, search up how to do two - step equations

To find the average income of an adult in the United States, 250 workers in Tennessee are questioned. No; the sample is not selected from the population to be studied.
No; the sample is not random.
Yes; the sample is selected at random from the population to be studied.

No; the sample is not selected from the population to be studied.

Explanation:

In statistics and quantitative research philosophy, a sample is a lot of people or articles gathered or chose from a factual populace by a characterized method. The components of an example are known as test focuses, inspecting units or perceptions.

In the sample that has been taken above in this question is not the appropriate sample to solve the purpose of the average. Because the purpose is to solve for the population of the whole country but sample is not taken from the whole country.

Bob went to the store and bought 10 apples if each apple was 5 dollars how much is the total cost

\$50

Step-by-step explanation:

Bob bought 10 apples

If 1 cost \$5

Total cost of the ten apples will be = \$5 x 10

= \$50

The ten apples cost \$50

\$50 was the price of the apples from the store

A store has a total supply of 250 pairs of shoes the shoes are selling at a rate of 10 Paris every hour the store has already sold 177 Paris of shoes

17 hours and 42 minutes.

Step-by-step explanation:

the store has a total supply of 250 pairs of shoes which sells 10 pairs of shoes every hour and it has already sold 177 pairs of shoes. So to find out the time needed to sell 177 pairs at a constant rate of 10 pairs every hour.

177 pairs = 17,7 hours or 17 hours and 42 minutes (70% off 60 = 42).

Two pump are used to empty a sewage tank. One pump pumps 60 gallons per minute (gpm) and the second pumps 50 gpm. They pumped for 30 minutes. How many total gallons are pumped

3,330 that’s the answer

Tomika uses 6 1/9 inches of wire to make a necklace and 3 1/3 inches of wire to make a bracelet how many necklace and bracelet sets can she make if she uses 28 1/3 inches of wire in all?

The answer is 3 necklaces and bracelets sets she can make

Solution:

Given that,

Length of wire used to make a necklace is:

Length of wire used to make a bracelet is:

Given that she uses 28 1/3 inches of wire in all

The answer is 3 necklaces and bracelets sets she can make

The following observations 40, 42, 45, x-1, x +1, 51, 54, 62 are arranged in ascending order.
If the median is 49, find the value of 'x'.
Hence find the mean of the above observations.​

(Video) Class - 10th, Ex - 1 Theorem 1.4(Real Numbers) NCERT CBSE prove root 2 irrational

Step-by-step explanation:

Here n = 8 (even number)

On the popular cooking show Cookbook Crunch, the host picks a random recipe from a cookbook and the author has to feed the 63-member studio audience in one hour! The host selects this recipe for Carlita: Spicy Spinach and Apricots (Feeds 6) Ingredients: • 1/2 kilogram spinach • 1/4 kilogram apricots • 1/5 kilogram jalapeno pastry • 1/10 kilogram pine nuts • Salt, pepper, and hot sauce Bake at 350° in a medium loaf pan for 45 minutes. Carlita only finds a hundred small, 175-gram loaf pans. If cooking time is proportional to the amount of mixture and if the oven holds 9 of these pans at once, how much time will be left in the show when Carlita pulls the last batch out of the oven? (Assume the time to mix ingredients, remove a batch from the oven, and put in the next one is insignificant.)​

3o mins!

Step-by-step explanation:

Ramu observed that in order toclimb a 12 meter high wall, he requires either a 13meter or a 20 meter long ladder if he keeps them at distances of x and y respectively from the foot of the wall assume that the ladders just touch the top of the wall what is the value of x + y?​ pls tell fast will mark brainliest

21 meters

Step-by-step explanation:

Step 1 :

Let x be the distance at which the 13 meter ladder is placed . We can consider this as a triangle with one angle as 90°, where the ladder is the hypotenuse and the wall is one side. We need to find the 3rd side x.

Using Pythagoras theorem, we have

13² = 12² + x² => 169 = 144 + x² => x² = 169-144 = 25

=> x = 5 meters

Step 2 :

Similarly ,

Let y be the distance at which the 20 meter ladder is placed . We can consider this as a triangle with one angle as 90°, where the ladder is the hypotenuse and the wall is one side. We need to find the 3 rd side which is y.

Using Pythagoras theorem, we have

i.e 20² = 12² + y² => 400 = 144 + y² => y² = 200-144 = 256

=> y = 16 meters

Step 3 :

Value of x + y = 5 + 16 = 21 meters

If f(x)=x+3, g(x)=2x+6, and h(x)=x^2+6x+9, then (f-g)(4)= ?

Step-by-step explanation:

10. The lengths of two sides of a right triangle are given. Find the length of the third side. Round to the nearest tenth if necessary. legs: 24 in. and 16 in.
A. 17.9 in.
B. 28.8 in.
C. 34.7 in.
D. 31 in

it's B 28.8 in

Step-by-step explanation:

Step-by-step explanation:

Length of third side

Or

Length of third side

You have \$700 to invest in an account and need to have \$950 in one year. What interest rate would you need to have in order to reach this goal if the amount is compounded quarterly? Round your answer to the nearest percent. Please Help.

(Video) Proof that Square Root 2 is Irrational

The interest rate would be 31.7%.

How to find the interest rate?

Here's the simple interest formula: Interest = P x R x N. P = Principal amount (the beginning balance). R = Interest rate (usually per year, expressed as a decimal).

(950-700)/700

1650+ years

Solve r = n(A/P)^1/nt - n

Simple interest is interest calculated on the predominant portion of a mortgage or the authentic contribution to a savings account. Simple interest does now not compound, which means that an account holder will only advantage interest on the fundamental, and a borrower will in no way ought to pay interest on interest already amassed.

#SPJ2

31.7%

Step-by-step explanation:

(950-700)/700

1650+ years

Solve r = n(A/P)^1/nt - n

You invest \$300 in an account that has a annual interest rate of 6%, compounded quarterly for four years. What is the equivalent interest rate, and how many times will the money be compounded? Please Help.

16

Step-by-step explanation:

quarterly means every 3 month , so there are 4 quarterlies in one year . 4 multiplied by 4 years = 16. So there are 16 quarterlies in 4 years. Therefore, \$300 will be compounded 16 times for four years.

An island population of 20,000, grows by 5% each year, compounded continuously. How many inhabitants will the island have in 5 years according to the exponential growth function? Round your answer down to the nearest integer

25680

Step-by-step explanation:

A=Pe^rt

A=20000e^((0.05)(5))

A=20000e^(.25)

A=25680.508

A population of 20,000 growing at a constant rate of 5%

What additional information would prove that LMNP is a rectangle?

if the length of LMNP was greater than the width

2 pairs of congruent sides, 2 pairs of parallel sides, 4 90° angles.

Other Questions

(Video) prove that root 2 is an irrational number | root 2 is irrational number | root 2 is not rational |

## FAQs

### How do you prove that √ 2 is an irrational number? ›

√2 = p/q, where 'p' and 'q' are integers, q ≠ 0 and p, q have no common factors (except 1). Thus, p and q have a common factor 2. This statement contradicts that 'p' and 'q' have no common factors (except 1). We can say that √2 is not a rational number.

Is √ 2 a irrational number? ›

Sal proves that the square root of 2 is an irrational number, i.e. it cannot be given as the ratio of two integers.

How do you prove √ 2 √ 5 is irrational? ›

To prove that √2 + √5 is an irrational number, we will use the contradiction method. ⇒ We know that (p2/q2 - 7) / 2 is a rational number. Also, we know √10 = 3.1622776... which is irrational. Since we know that √10 is an irrational number, but an irrational number cannot be equal to a rational number.

How do you prove √ 2 3 is irrational solution? ›

∴ √2/ 3 = p/q where p and q are some integers and HCFp q = 1 ….. 1From 2 and 3 2 is a common factor of both p and q which contradicts 1. Hence our assumption is wrong. Thus √2 3 is irrational.

How do you prove root 2 is irrational Wikipedia? ›

Despite having a smaller denominator, it is only slightly less accurate than the Babylonian approximation. Pythagoreans discovered that the diagonal of a square is incommensurable with its side, or in modern language, that the square root of two is irrational.

Is √ 2 a real number? ›

√2 is irrational. Now we know that these irrational numbers do exist, and we even have one example: √2. It turns out that most other roots are also irrational.

## Videos

1. A-Level Maths: A1-11 Proving √2 is Irrational
(TLMaths)
2. Theorem 1.4 | Root 2 is irrational. Chapter 1-Real Number Class 10th in hindi
(math universe)
3. Prove That 3+2√5 is irrational | Ex 1.3 Q 2 Class 10 Maths Real Numbers | Link in- √3 is irrational​
(NCERT GyanKosh)
4. How do we Plot Root 2 on a Number Line? | Irrational Numbers | Don't Memorise
(Infinity Learn Class 9&10)
5. How to prove the square root of 2 is a irrational number ?
6. Root 2 - Numberphile
(Numberphile)

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