Answer

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**Hint:**

Here, we will do the prime factorization of the given number. Factorization is a method of writing an original number as the product of its various factors. We will consider a pair of the same numbers as a single number because we are required to find the square root. Hence, multiplying the remaining factors, we would find the required square root of the given number.

**Complete step by step solution:**

In this question, first of all, we are required to do the prime factorization of 256.

Prime numbers are those numbers which are greater than 1 and have only two factors, i.e. factor 1 and the prime number itself.

Hence, prime factorization is a method in which we write the original number as the product of various prime numbers.

Therefore, prime factorization of 256 is:

We can see that 256 is an even number, so dividing it by the least prime number 2, we get

\[256 \div 2 = 128\]

Dividing 128 by 2, we get

\[128 \div 2 = 64\]

Dividing 64 by 2, we get

\[64 \div 2 = 32\]

Dividing 32 by 2, we get

\[32 \div 2 = 16\]

Dividing 16 by 2, we get

\[16 \div 2 = 8\]

Dividing 8 by 2, we get

\[8 \div 2 = 4\]

Dividing 4 by 2, we get

\[4 \div 2 = 2\]

Now as we get the quotient as a prime number, so we will not divide the number further.

Hence, 256 can be written as:

\[256 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2\]

Now, since we are required to find the square root, we would take only one prime number out of a pair of the same prime numbers.

\[ \Rightarrow \sqrt {256} = 2 \times 2 \times 2 \times 2\]

\[ \Rightarrow \sqrt {256} = 16\]

Hence, the square root of 256 is 16.

**Therefore, the required answer is 16.**

**Note:**

If in the question, it was not mentioned that we are required to use the factorization method, then we could have used the ‘Repeated Subtraction Method’ in which we subtract \[1,3,5,...\] from the number in every next step till we get a \[0\] and the number of steps is equal to the square root of the number.

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