Question

Find the value of the square root of $({26}^2-{24}^2)\times 4$.

• A. $400$
• B. $100$
• C. $10$
• D. $20$

Answer 1

The correct option is D $20$

$\underset{–}{\text{Need to Find:}}$
Square root of $({26}^2-{24}^2)\times 4$, i.e., $\sqrt{({26}^2-{24}^2)\times 4}$

First, let's simplify ${26}^2-{24}^2$

${26}^2-{24}^2=(26+24)(26-24)$ $[\because a^2-b^2=(a+b\left)\right(a-b\left)\right]$

$\Rightarrow {26}^2-{24}^2=50\times 2=100$

$\therefore ({26}^2-{24}^2)\times 4=100\times 4$

$\Rightarrow ({26}^2-{24}^2)\times 4=400$

Taking square root both the sides:

$\Rightarrow \sqrt{({26}^2-{24}^2)\times 4}=\sqrt{400}$

Now, we need to find the square root of $400$.

$\sqrt{400}={400}^{\frac{1}{2}}=(20\times 20{)}^{\frac{1}{2}}=({20}^2{)}^{\frac{1}{2}}$
$\therefore \sqrt{400}={20}^{2\times \frac{1}{2}}=20$

$\Rightarrow \underset{–}{\sqrt{({26}^2-{24}^2)\times 4}=20}$

Hence, the square root of $({26}^2-{24}^2)\times 4$ is $20$.

$\therefore$ Option (d.) is the correct answer.