Question

If the cube root of n is 4, then find the square root of n.
(a). 4
(b). 6
(c). 8
(d). 16

Answer 1

Hint: The cube root of a number is given. To find the number, just take the cube of the given number. Then you can find the square root of the obtained number by using the prime factorization method.

Complete step-by-step answer:
Cube root of a number is the number which when multiplied with itself three times gives the original number. For example, the cube root of 8 is 2.
The square root of a number is the number which when multiplied with itself gives the original number. For example, the square root of 4 is 2.
Now, we are given that the cube root of some number n is 4. Then, the number n is a cube of 4, hence, we have:
\[n = {4^3}\]
We know that the cube of 4 is 64, hence, we have:
\[n = 64\]
Now, we need to find the square root of the number 64. We can find the square root using the prime factorization method.
In this method, we take the number and divide it by the first prime number 2, until we get a remainder and then, we divide with the next prime number and so on until we get the final number as 1.
The prime factors of 64 are found as follows:

Pairing the factors of 64, we have:
\[64 = \underline {2 \times 2} \times \underline {2 \times 2} \times \underline {2 \times 2} \]
Now, taking the square root, we have:
\[\sqrt {64} = 2 \times 2 \times 2\]
\[\sqrt {64} = 8\]
Hence, the correct answer is option (c).

Note: You may choose option (d) as the correct answer by misinterpreting the term square and the number 4 and square 4 to get 16 but it is wrong.