Question

Find the square root of 7056 by factorization method

Answer 1

Answer:

Let us first calculate the prime factors of 7056 by the method of prime factorisation.

⇒ 7056 = 2 × 2 × 2 × 2 × 3 × 3 × 7 × 7

Writing them in terms of power we get,

⇒ 7056 = 2⁴ × 3² × 7²

Now square root of 7056 is nothing but multiplying half to the power of all the prime factors. That is,

$\implies \sqrt{7056} = \sqrt{2^4} \times \sqrt{3^2} \times \sqrt{7^2}\\\\\implies 7056^{(0.5)} = 2^{(4\times0.5)} \times 3^{(2\times0.5)} \times 7^{(2\times0.5)}\\\\\implies \sqrt{7056} = 2^2 \times 3 \times 7\\\\\implies \sqrt{7056} = 4 \times 3 \times 7 = 84$

Hence the square root of 7056 is 84.

Answer 2

$\sqrt{7056}$

$\mathrm{Factor\:the\:number:\:}\:7056=84^2$

$=\sqrt{84^2}$

$\mathrm{Apply\:radical\:rule}:\quad \sqrt{a^2}=a,\:\quad \:a\ge 0$

$\sqrt{84^2}=84$

$=84$