Question

question 11 (1 point) state the side length of a square with an area of 147 cm² in simplified radical form. a) 7√3 cm b) $\frac{147}{sqrt{2}}$ cm c) $sqrt{137}$ cm d) $\frac{147}{2}$ cm

Explanation:

Step1: Recall area formula for square

Let the side - length of the square be $s$. The area formula of a square is $A = s^{2}$. Given $A = 147\ cm^{2}$, so $s^{2}=147$.

Step2: Solve for $s$

Take the square - root of both sides: $s=\sqrt{147}$.

Step3: Simplify the radical

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 $\sqrt{49\times3}=\sqrt{49}\cdot\sqrt{3}=7\sqrt{3}\ cm$.

Answer:

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