Question

find the square root of the following number by the prime factorization method : 1764

Answer 1

2 | 1764

2 | 882

3 | 441

3 | 147

7 | 49

7 | 7

=> 1764 = 2 × 2 × 3 × 3 × 7 × 7

=> sqrt (1764) = 2 × 3 × 7

=> sqrt (1764) = 42

Answer 2

$\textbf{Solution :}$

$\textbf{Step 1}$

Find the prime factors of 1764 by prime factorisation method.

Kindly refer to the attachment

$\textbf{Step 2}$

Write down —

$\sqrt{1764} = \sqrt{prime \: factors \: of \: 1764} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \sqrt{2 \times 2 \times 7 \times 7 \times 3 \times 3 } \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2 \times 7 \times 3 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 14 \times 3 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 42$

So, $\textbf{Sq. root of 1764 = 42}$



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