Question

Find square root of 9604 by prime factorisation​

Answer 1

Answer:

Write prime factors of 9604 by using the prime factorization method.

Take square roots on both sides to get the square root of 9604.

9604=2 × 2 × 7 × 7 × 7 &times ;7 = 22×72×72.

Taking square root, we have.

9604=22×72×72.

= 2 ×7 ×7.

= 98.

Step-by-step explanation:

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Answer 2

$\large\underline{\sf{Solution-}}$

Given expression is

$\rm :\longmapsto\: \sqrt{9604}$

$\green{\rm :\longmapsto\:Prime \: factorization \: of \: 9604}$

$\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{2}}}&{\underline{\sf{\:\:9604 \:\:}}}\\ {\underline{\sf{2}}}& \underline{\sf{\:\:4802 \:\:}} \\\underline{\sf{7}}&\underline{\sf{\:\:2401\:\:}} \\ {\underline{\sf{7}}}& \underline{\sf{\:\:343 \:\:}} \\ {\underline{\sf{7}}}& \underline{\sf{\:\:49 \:\:}} \\ {\underline{\sf{7}}}& \underline{\sf{\:\:7 \:\:}} \\\underline{\sf{}}&{\sf{\:\:1 \:\:}} \end{array}\end{gathered}$

So,

$\green{\rm :\longmapsto\:Prime \: factorization \: of \: 9604 = 2 \times 2 \times 7 \times 7 \times 7 \times 7}$

Hence,

$\rm :\longmapsto\: \sqrt{9604}$

$\rm \:  =  \: \sqrt{ \underbrace{2 \times 2 }\times \underbrace{7 \times 7} \times \underbrace{7 \times 7}}$

$\rm \:  =  \: 2 \times 7 \times 7$

$\rm \:  =  \: 98$

Therefore,

$\rm\implies \:\boxed{\tt{ \: \: \sqrt{9604} = 98 \: \: }}$

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MORE TO KNOW

1. The square of any natural number can never ends with 2, 3, 7, 8 or odd number of zeroes.

2. The sum of first n odd natural numbers is equals to sum of square of number of terms.

3. Between squares of two consecutive natural numbers n and n + 1, there are 2n natural numbers.