Question

find the square root by prime factorization method
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Answer 1

Question :-

Find the square root of 8836 by prime factorization method.

Answer :-

The square root of 8836 is 94.

Solution:-

Prime factorization of 8836:-

$\begin{array}{r|l}\sf2&\sf8836\\\cline{2-2}\sf2&\sf4418\\\cline{2-2}\sf47&\sf2209\\\cline{2-2}\sf47&\sf47\\\cline{2-2}&\sf1\end{array}$

By prime factorization ,

8836 = 2 × 2 × 47 × 47

= 2 × 47

= 94

Therefore,

$\sqrt{8836} = 94$

Just do Verification :-

8836 = 94 × 94

Now,

( 94 )² = 8836

L.H.S = R.H.S

Hence, Proved

Hence ,

94 is the answer .

Additional Information :-

What is Prime Factorisation Method ?

Step 1: Start by dividing the number by the first prime number 2 and continue dividing by 2 until you get a decimal or remainder. Then divide by 3, 5, 7, etc. until the only numbers left are primenumbers.

Step 2: Write the number as a product of prime numbers.