Q:

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

Accepted Solution

A:
Answer:[tex]\large\boxed{8n^{18}}[/tex]Step-by-step explanation:The formula of an area of a square:[tex]A=s^2[/tex]s - side lengthWe have[tex]A=64n^{36}[/tex]Method 1:Substitute:[tex]s^2=64n^{36}[/tex][tex]s^2=8^2n^{18\cdot2}[/tex]            use [tex](a^n)^m=a^{nm}[/tex][tex]s^2=8^2(n^{18})^2[/tex]         use [tex](ab)^n=a^nb^n[/tex][tex]s^2=(8n^{18})^2\to s=8n^{18}[/tex]Method 2:Substitute:[tex]s^2=64n^{36}\to s=\sqrt{64n^{36}}[/tex]   use [tex]\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}[/tex][tex]s=\sqrt{64}\cdot\sqrt{n^{36}}[/tex][tex]s=8\sqrt{n^{(18)(2)}[/tex]     use [tex](a^n)^m=a^{nm}[/tex][tex]s=8\sqrt{(n^{18})^2}[/tex]      use [tex]\sqrt{a^2}=a[/tex] for [tex]a\geq0[/tex][tex]s=8n^{18}[/tex]