Question

question 24 (1 point) state the side length of a square with an area of 147 cm² in simplified radical form. a) 7√3 cm b) √147/12 cm c) √137 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. Given $A = 147\ cm^{2}$, we have $s^{2}=147$.

Step2: Solve for side - length

Taking the square root of both sides, $s=\sqrt{147}$.

Step3: Simplify the square root

Factor 147: $147 = 49\times3$. Then $\sqrt{147}=\sqrt{49\times3}$. Using the property $\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}$ ($a = 49$, $b = 3$), we get $\sqrt{49}\cdot\sqrt{3}=7\sqrt{3}\ cm$.

Answer:

a) $7\sqrt{3}\ cm$