Question

The area of a square is 64n^36 units. What is the side length of one side of the square? 8n^6 8n^18 64n^6 64n^18

Answer 1

`\large\boxed{8n^(18)}`

Explanation:

The formula of an area of a square:

`A=s^2`

s - side length

We have

`A=64n^(36)`

Method 1:

Substitute:

`s^2=64n^(36)`

`s^2=8^2n^(18\cdot2)` use
`(a^n)^m=a^(nm)`

`s^2=8^2(n^(18))^2` use
`(ab)^n=a^nb^n`

`s^2=(8n^(18))^2\to s=8n^(18)`

Method 2:

Substitute:

`s^2=64n^(36)\to s=\sqrt{64n^(36)}` use
`√(ab)=√(a)\cdot√(b)`

`s=√(64)\cdot\sqrt{n^(36)}`

`s=8\sqrt{n^((18)(2))` use
`(a^n)^m=a^(nm)`

`s=8\sqrt{(n^(18))^2}` use
`√(a^2)=a` for
`a\geq0`

`s=8n^(18)`