Question

Evaluate the given value: $\sqrt {4096} $

Answer 1

Hint: In the above question, we are asked to calculate the square root of the number. This can be achieved by resolving the given number into a product of its prime factor and then by taking the square root on both the sides.

Complete step-by-step answer:
We have the given value as

$ = \sqrt {4096} $

After resolving 4096 into product of prime factors, we get

2|4096
______
2|1024
______
2|512
______
2|256
______
2|128
______
2|64
______
2|32
______
2|16
______
2|8
______
2|4
______
2

Therefore, we have

$4096 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2$
$\sqrt {4096} = \sqrt {2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2} $

$\sqrt {4096} = {\sqrt {{{(2 \times 2 \times 2 \times 2 \times 2)}^2}} ^{}}$

$\sqrt {4096} = 2 \times 2 \times 2 \times 2 \times 2$

$\therefore \sqrt {4096} = 64$

Hence, we have the required solution$\sqrt {4096} = 64$.

Note: When we face such a type of problem, we must have an adequate knowledge of the prime factorization of the numbers. We must find the prime factors carefully. We should not jump over any step, as this may lead to wrong factors and thus the wrong solution.