Question

What is the simplified form of square root of 144x^36?

Answer 1

Answer:

Option (b) is correct.

Expression becomes $=12x^{18}$

Step-by-step explanation:

Given : square root of $144x^{36}$

We have to write the given expression in simplified form.

Consider the given expression square root of $144x^{36}$

Mathematically written as $\sqrt{144x^{36}}$

$\mathrm{Apply\:radical\:rule\:}\sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b},$

We have,

$=\sqrt{144}\sqrt{x^{36}}$

We know $\sqrt{144}=12$

$=12\sqrt{x^{36}}$

$\mathrm{Apply\:radical\:rule\:}\sqrt[n]{a^m}=a^{\frac{m}{n}},\:\quad \mathrm{\:assuming\:}a\ge 0$

$\sqrt{x^{36}}=x^{\frac{36}{2}}=x^{18}$

Thus, Expression becomes $=12x^{18}$

Answer 2

Answer:

The correct option is B.

Step-by-step explanation:

The given expression is

$\sqrt{144x^{36}}$

Use the property of radicals.

$\sqrt{ab}=\sqrt{a}\sqrt{b}$

$\sqrt{144x^{36}}=\sqrt{144}\times \sqrt{x^{36}}$

Use the property of exponent.

$a^{mn}=(a^m)^n$

$\sqrt{144x^{36}}=12\times \sqrt{(x^{18})^2}$

$\sqrt{144x^{36}}=12\times x^{18}$

$\sqrt{144x^{36}}=12x^{18}$

Therefore option B is correct.