Square root and cube root

user November 19, 2023

(6) What is the cube root of 64?

(a) 4
(b) 6
(c) 8
(d) 10

Correct Answer: (a) 4
The cube root of 64 is $ \sqrt[3]{64} = 4 $.
$\sqrt[3]{64} = 4$

(7) If the square root of a number is 7, what is the cube root of the square of that number?

(a) 7
(b) 21
(c) 49
(d) 343

Correct Answer: (c) 49
If the square root of a number is 7, then the number itself is $7^2 = 49$. The cube root of the square of this number is $ \sqrt[3]{49^2} $.
$\sqrt[3]{49^2} = \sqrt[3]{2401} = 49$

(8) What is the smallest integer that when squared gives a number greater than 2500?

(a) 49
(b) 50
(c) 51
(d) 52

Correct Answer: (c) 51
The smallest integer whose square is greater than 2500 is 51 since $50^2 = 2500$ and $51^2 = 2601$.
$51^2 = 2601 > 2500$

(9) What is the cube root of 27?

(a) 2
(b) 3
(c) 4
(d) 5

Correct Answer: (b) 3
The cube root of 27 is $ \sqrt[3]{27} = 3 $.
$\sqrt[3]{27} = 3$

(10) If the square of a number is 64, what is the cube root of that number?

(a) 2
(b) 4
(c) 8
(d) 16

Correct Answer: (c) 8
If the square of a number is 64, then the number itself is $ \sqrt{64} = 8 $. The cube root of this number is $ \sqrt[3]{8} $.
$\sqrt[3]{8} = 2$

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