Question

The monomial 36x4 is a perfect square. What is the square root of 36x4

Answer 1

Well 36x4=144

So you have do this equation

36x4=144√=12


So the square root of 144 or 36x4 is 12

Answer 2

The square root of
`36x^4` is
`6x^2`.

Explanation:

To find the square root of
`36x^4` you must apply the radical rule
`\sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b},\:\quad \mathrm{\:assuming\:}a\ge 0,\:b\ge 0`

`√(36x^4)=√(36)√(x^4)`

`√(36x^4)=√(6^2)√(x^4)\\\\√(36x^4)=6√(x^4)\\\\√(36x^4)=6√(\left(x^2\right)^2)`

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

`√(36x^4)=6√(\left(x^2\right)^2)\\\\√(36x^4)=6x^2`