Question

Find the square root of $1,764$ using prime factorization method.

• A. $32$
• B. $38$
• C. $42$
• D. $48$

Answer 1

The correct option is C $42$

Step 1:
Represent the given number using its prime factors as elaborated below

$\therefore 1764=2\times 2\times 3\times 3\times 7\times 7$

Step 2:
Pair-up the prime factors
$\therefore 1764=\left(\underset{–}{2\times 2}\right)\times \left(\underset{–}{3\times 3}\right)\times \left(\underset{–}{7\times 7}\right)$

Step 3:
Choose one prime factor from each pair and make the product to find the square root of the given number
$\therefore \underset{–}{\sqrt{1764}=2\times 3\times 7=42}$

Hence, option (c.) is the correct one.