Question

find the square root of 20657025 by prime factorization ​

Answer 1

Solution:—

First let's find the prime factorization of 20657025 :-

$\begin{array}{r|l}\sf5&\sf20657025\\\cline{2-2}\sf5&\sf4131405\\\cline{2-2}\sf3&\sf826281\\\cline{2-2}\sf3&\sf275427\\\cline{2-2}\sf3&\sf91809\\\cline{2-2}\sf3&\sf30603\\\cline{2-2}\sf3&\sf10201\\\cline{2-2}\sf101&\sf10201\\\cline{2-2}\sf101&\sf101\\\cline{2-2}&\sf1\end{array}$

20657025 = 5 × 5 × 3 × 3 × 3 × 3 × 101 × 101

= 5 × 3 × 3 × 101

= 15 × 3 × 101

= 45 × 101

= 4,545

$\sf{Answer:- \: 4,545 \: \purple{ \bigstar}}$

$\underline{ \sf{Therefore, \: \sqrt{20657025} = 4545 }}$

Required Answer:-

The square root of 20657025 by prime factorization is 4545.

More Info:—

• If the numbers are composite, they can be spilt up further till all the factors are prime numbers. Such factorization is called prime factorization.
• The square of a number is that number raised to the power 2.
• A natural number is called a perfect square, if it is the square of some natural number.