Question

question 7 (1 point) state the side length of a square with an area of 147 cm² in simplified radical form.
a) 7√3 cm
b) √137 cm
c) 147/√2 cm
d) 147/2 cm

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.

Step2: Solve for side - length

Given $A = 147\mathrm{cm}^{2}$, we have $s=\sqrt{A}$. So $s = \sqrt{147}$.

Step3: Simplify the square root

We factor 147: $147=49\times3$. Then $\sqrt{147}=\sqrt{49\times3}=\sqrt{49}\times\sqrt{3}=7\sqrt{3}\mathrm{cm}$.

Answer:

A. $7\sqrt{3}\text{ cm}$