Question

What is a simpler form of the radical expression root36g^6

Answer 1

The simpler form of the radical expression
`√(36g^6)` is
`6g^3`.

Explanation:

To find the simpler form of the expression
`√(36g^6)`.

Apply the radical rule
`\sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b},\:\quad \mathrm{\:assuming\:}a\ge 0,\:b\ge 0`

`√(36)√(g^6)`

We have that
`√(36)=6`, so
`√(36g^6)=6√(g^6)`

Next, apply the exponent rule
`a^(bc)=\left(a^b\right)^c`

`g^6=g^(3\cdot \:2)=\left(g^3\right)^2`

`√(36)√(g^6)=6√(\left(g^3\right)^2)`

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

`√(\left(g^3\right)^2)=g^3`

Therefore,

`√(36g^6)=6g^3`

Answer 2

we know that
√[36*g^6]
=√[6²*(g³)²]
=(√6²)*(√[(g³)²])
=6*g³

the answer is
6*g³