Question

Exploring Square Roots and Rational Numbers ( PLEASE HELP )

Answer 1

ok so here ur supposed to figure out which two perfect squares does the square/rational root fall between… an example of a perfect square is square root of 64, since u multiply 8*8 to get 64… another example is square root of 49 since u multiply 7*7.

it’s a pretty easy topic… i’m sure u will get the hang of it :)

Answer 2

(To simplify the answers, I will refer to the first sentence of the question as part A and the second sentence as part B.)

Question 17

Part A: the square root is between 6 and 7

Part B: the square root is 6.5

Question 18

Part A: the square root is between 9 and 10

Part B: the square root is 9.4

(Extra: the answer in simplified radical form is 2√22)

Question 19

Part A: the square root is between 7 and 8

Part B: the square root is 7.9

(Extra: the answer in simplified radical form is 3√7)

Question 20

Part A: the square root is between 8 and 9

Part B: the square root is 8.7

(Extra: the answer in simplified radical form is 5√3)

Question 21

Part A: the square root is between 5 and 6

Part B: the square root is 5.5

Question 22

Part A: the square root is between 9 and 10.

Part B: the square root is 9.8

Explanation:

First of all, it says you can use a calculator! If you do not know how to, let me know in the comments and I can try to help you out! Read the explanation to understand how to do this.

Question 17

Using a calculator, you get 6.48074069… for your decimal.

Rounding it to the nearest tenth, your answer would be 6.5

Now, to find the two consecutive whole numbers the square root is between…

However, there is another way to do this. Remember that 7x7=49. We know that 49 is greater than 42, so let’s see try out a number smaller than 7! 6x6=36. 42 is between 36 and 49, so the square root is between 6 and 7.

Another way to do this is… we know that the decimal is about 6.5, which is between 6 and 7, since those are the two whole numbers before and after that decimal!

Question 18

Using a calculator, you get 9.380833151… for your decimal.

This rounds to 9.4

The whole numbers surrounding this decimal are 9 and 10.

You can also do this by knowing that 9x9, or 9^2, is 81 and 10x10, or 10^2, is 100, and those are the numbers surround 88.

In non-decimal form (simplified radical), your answer can be 2√22.

Question 19

Using a calculator, you get 7.93725393… for your decimal.

This rounds to 7.9

The whole numbers surrounding this decimal are 7 and 8.

You can also do this by knowing that 7x7, or 7^2, is 49 and 8x8, or 8^2, is 64, and those are the numbers surround 63.

In non-decimal form (simplified radical), your answer can be 3√7.

Question 20

Using a calculator, you get 8.66025403… for your decimal.

This rounds to 8.7

The whole numbers surrounding this decimal are 8 and 9.

You can also do this by knowing that 8x8, or 8^2, is 64 and 9x9, or 9^2, is 81, and those are the numbers surround 75.

In non-decimal form (simplified radical), your answer can be 5√3.

Question 21

Using a calculator, you get 5.47722557… for your decimal.

This rounds to 5.5

The whole numbers surrounding this decimal are 5 and 6.

You can also do this by knowing that 5x5, or 5^2, is 25 and 6x6, or 6^2, is 36, and those are the numbers surround 30.

Question 22

Using a calculator, you get 9.84885780… for your decimal.

This rounds to 9.8

The whole numbers surrounding this decimal are 9 and 10.

You can also do this by knowing that 9x9, or 9^2, is 81 and 10x10, or 10^2, is 100, and those are the numbers surround 97.

Note: the symbol "^" means that the number following that symbol is an exponent. So 2^2 is 2 squared,
`2^2`, or 2 to the power of 2.

Hope that helps! <3

Disclaimer: I am not responsible for anything you get incorrect, as I only have the context and information you provide, and I give my response based on my knowledge supported with credible information from experts and online professional articles.