Square root and cube root

user November 19, 2023

(1) If the square root of a number is 11, what is the cube of that number?

(a) 121
(b) 1331
(c) 14641
(d) 161051

Correct Answer: (c) 14641
If the square root of a number is 11, then the number itself is $11^2 = 121$. The cube of this number is $121^3$.
$121^3 = 11^2 \times 11^2 \times 11^2 = 11^6 = 14641$

(2) What is the cube root of one-eighth (1/8)?

(a) 1/2
(b) 1/3
(c) 1/4
(d) 2/3

Correct Answer: (b) 1/3
The cube root of one-eighth $(1/8)$ is equal to the cube root of $(1/2)^3$.
$\sqrt[3]{\frac{1}{8}} = \sqrt[3]{\left(\frac{1}{2}\right)^3} = \frac{1}{2}$

(3) What is the smallest integer that when squared gives a number greater than 1000?

(a) 32
(b) 31
(c) 30
(d) 29

Correct Answer: (a) 32
The smallest integer whose square is greater than 1000 is 32 since $31^2 = 961$ and $32^2 = 1024$.
$32^2 = 1024 > 1000$

(4) If the cube root of a number is 5, what is the square of that number?

(a) 15
(b) 25
(c) 125
(d) 625

Correct Answer: (c) 125
If the cube root of a number is 5, then the number itself is $5^3 = 125$. The square of this number is $125^2$.
$125^2 = 5^3 \times 5^3 = 5^6 = 15625$

(5) What is the square root of 144?