Question

8.EE.1.2

Which expressions have a value that is between 9 and 10. Select all that apply.

A.) √80

B.) √89

C.) √101

D.) 3 √725

E.) 3 √750

F.) 3 √999

G.) 3 √1010

Answer 1

Considering that the square root of 9 is of 81 and of 10 is of 100, we have that the expression that has a value between 9 and 10 is given by:

B.) √89

E.) $\sqrt[3]{750}$

F.) $\sqrt[3]{999}$

How the square root of a number is used to solve this question?

We suppose numbers n and m, with square roots given, respectively, by n² and m².

Then, the square roots of all numbers between n² and m² have values between n and m.

In this problem, the square roots are given by:

• 9² = 81.

• 10² = 100.

Hence, the square root of all values between 82 and 99 are values between 9 and 10, thus option B is correct.

As for the cubic root, we apply the same logic and have that:

• 9³ = 729.

• 10³ = 1000.

Hence options E and F are also correct, as the values between 730 and 999 have cubic roots between 9 and 10.

More can be learned about the value of a expression at https://brainly.com/question/25537936

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