Question

a square has an area of 18x² square inches. what is the length of one of its sides? 9x√2 3√2x 3x√2 9x

Explanation:

Step1: Recall area formula for square

The area formula of a square is $A = s^{2}$, where $A$ is the area and $s$ is the side - length. Given $A = 18x^{2}$.

Step2: Solve for side - length $s$

We set $s^{2}=18x^{2}$. Taking the square root of both sides, $s=\sqrt{18x^{2}}$.

Step3: Simplify the square - root expression

We know that $\sqrt{18x^{2}}=\sqrt{9\times2\times x^{2}}$. Using the property $\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}$ ($a = 9x^{2}$, $b = 2$), we get $s = 3x\sqrt{2}$.

Answer:

$3x\sqrt{2}$