Question

Find the square root of the following number by the prime factorization method 4096.

Answer 1

Hint: Since this number is clearly divisible by 2, so, its prime factors will include 2’s only. After obtaining the number of two’s, take the square root and proceed with the calculation till the final number whose square is equal to 4096 is obtained.

Complete step by step answer:
By prime factorisation method, we have
4096 = 2×2×2×2×2×2×2×2×2×2×2×2
\[ \Rightarrow 4096 = {2^2} \times {2^2} \times {2^2} \times {2^2} \times {2^2} \times {2^2}\]
Taking square root on both the sides, we have
\[
   \Rightarrow \sqrt {4096} = \sqrt {{2^2} \times {2^2} \times {2^2} \times {2^2} \times {2^2} \times {2^2}} \\
   = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \\
   = 64 \\
\]
∴ The square root of 4096 is 64.

Note: prime factors (a factor that is a prime number) : Any of the prime numbers that can be multiplied to give the original number are called prime factors. Prime numbers are the numbers that have only two factors one and themselves.