Question

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

A.) 12x^6
B.) 12x^18
C.) 72x^6
D.) 72x^18

Answer 1

Option (b) is correct.

Expression becomes
`=12x^(18)`

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,

`=√(144)\sqrt{x^(36)}`

We know
`√(144)=12`

`=12\sqrt{x^(36)}`

`\mathrm{Apply\:radical\:rule\:}\sqrt[n]{a^m}=a^{(m)/(n)},\:\quad \mathrm{\:assuming\:}a\ge 0`

`\sqrt{x^(36)}=x^{(36)/(2)}=x^(18)`

Thus, Expression becomes
`=12x^(18)`

Answer 2

The correct option is B.

Explanation:

The given expression is

`\sqrt{144x^(36)}`

Use the property of radicals.

`√(ab)=√(a)√(b)`

`\sqrt{144x^(36)}=√(144)* \sqrt{x^(36)}`

Use the property of exponent.

`a^(mn)=(a^m)^n`

`\sqrt{144x^(36)}=12* \sqrt{(x^(18))^2}`

`\sqrt{144x^(36)}=12* x^(18)`

`\sqrt{144x^(36)}=12x^(18)`

Therefore option B is correct.