Question

Area of a square is $125{\text{cm}}^2$. What is the length of the side of the square? Is the length obtained a surd?

• A. $5\sqrt{5}\text{cm}$, yes
• B. $5\sqrt{25}\text{cm}$, no
• C. $25\sqrt{5}\text{cm}$, yes
• D. $25\text{cm}$, no

Answer 1

The correct option is A $5\sqrt{5}\text{cm}$, yes

Let the length of the side of the square be $a\text{cm}$
Area of square $={\text{side}}^2=a^2$
Since area is given as $125{\text{cm}}^2$
Hence,
$a^2=125$
Taking square root of both sides, we get
$\sqrt{a^2}=\sqrt{125}$
$a=\sqrt{5^3}$
$\therefore$ The length of the side of the square $a$ is $5\sqrt{5}\text{cm}$ which can not be simplified into a p/q form where $q\ne 0$ and thus length of the square is a surd.