Question

Find the square root of $784$.

• A. $14$
• B. $18$
• C. $24$
• D. $28$

Answer 1

The correct option is D $28$

$\underset{–}{\text{First Method:}}$

Applying the prime factorization method to find the square root of $784$:

$784=2\times 2\times 2\times 2\times 7\times 7$
$\Rightarrow 784=2^4\times 7^2$

Taking the square root both the sides, we get:

$\Rightarrow \sqrt{784}=\sqrt{2^4\times 7^2}$
$\Rightarrow \sqrt{784}=(2^4\times 7^2{)}^{\frac{1}{2}}$
$\Rightarrow \sqrt{784}=(2^4{)}^{\frac{1}{2}}\times (7^2{)}^{\frac{1}{2}}$ $[\because (a\times b{)}^n=a^n\times b^n]$

$\Rightarrow \sqrt{784}=(2{)}^{4\times \frac{1}{2}}\times (7{)}^{2\times \frac{1}{2}}$
$[\because (a^m{)}^n=a^{m\times n}]$

$\Rightarrow \underset{–}{\sqrt{784}=2^2\times 7=2\times 2\times 7=28}$

$\underset{–}{\text{Second Method:}}$

Square root of $784$ using long division method can be evaluated as:


Hence, the square root of $784$ is $28$.

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