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

Answer:

$\large\boxed{8n^{18}}$

Step-by-step 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 $\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}$

$s=\sqrt{64}\cdot\sqrt{n^{36}}$

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

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

$s=8n^{18}$