Question

Determine the side of a square whose area is $4\sqrt{125}{\text{unit}}^2.$

• A. $2\left(5\sqrt{5}\right)\text{unit}$
• B. $2(5\sqrt{5}{)}^{\frac{1}{2}}\text{unit}$
• C. $5(5\sqrt{5}{)}^{\frac{1}{2}}\text{unit}$
• D. $2(5\sqrt{5}{)}^{\frac{1}{2}}{\text{unit}}^2$

Answer 1

The correct option is B $2(5\sqrt{5}{)}^{\frac{1}{2}}\text{unit}$

Let the side of a square be ${}^{\prime }{a}^{\prime }.$

We know, Area $=a\times a$
$\Rightarrow 4\sqrt{125}=a^2$
(taking square root of both side of the equation)
$\Rightarrow (4\sqrt{125}{)}^{\frac{1}{2}}=(a^2{)}^{\frac{1}{2}}$
$\Rightarrow (4{)}^{\frac{1}{2}}\times (\sqrt{5\times 5\times 5}{)}^{\frac{1}{2}}=a^{2\times \frac{1}{2}}$
$\Rightarrow a=2(5\sqrt{5}{)}^{\frac{1}{2}}$

$\therefore$ Side of the square is $2(5\sqrt{5}{)}^{\frac{1}{2}}\text{unit}.$