Question

Find the square root of the following $\frac{2025}{4900}$

• A. $\frac{55}{80}$
• B. $\frac{55}{70}$
• C. $\frac{45}{80}$
• D. $\frac{45}{70}$

Answer 1

The correct option is D $\frac{45}{70}$

Let us find the square root of $2025and4900$ by factorising them.
$3\mid 2025\overline{3\mid 675}\overline{3\mid 225}\overline{3\mid 75}\overline{5\mid 25}\overline{5\mid 5}\overline{\mid 1}$
$2025=\underset{–}{3\times 3}\times \underset{–}{3\times 3}\times \underset{–}{5\times 5}$
$\sqrt{2025}=3\times 3\times 5=45$
$2\mid 4900\overline{2\mid 2450}\overline{5\mid 1225}\overline{5\mid 245}\overline{7\mid 49}\overline{7\mid 7}\overline{\mid 1}$
$4900=\underset{–}{2\times 2}\times \underset{–}{5\times 5}\times \underset{–}{7\times 7}$
$\sqrt{4900}=2\times 5\times 7=70$
So, $\frac{\sqrt{2025}}{\sqrt{4900}}=\frac{45}{70}$.