Math, asked by amani9961, 8 months ago

Find the square root of 40.96 by prime factorization method.

Answers

Answered by a215114

Answer: Square root of 40.96 is 6.4

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Answered by Anonymous

✴ Square root of 40.96 is 6.4 ✴.

$\sqrt{40.96} = \sqrt{ \frac{4096}{100} } = \frac{ \sqrt{4096} }{ \sqrt{100} }$

Now, find the root of 4096 and 100 by prime factorization method [ See the attachment ],

Prime factorization of 4096,

We get,

$4096 = \underline {2 \times 2} \times \underline{2 \times 2} \times \underline {2 \times 2} \times \underline{8 \times 8}$

( Make the pairs of square).

$\sqrt{4096} = 2 \times 2 \times 2 \times 8$

$\sqrt{4096} = 64$

Now, from the prime factorization of 100 [ refer the attachment],

We get,

$100 = \underline {10 \times 10}$

$\sqrt{100 } = 10$

We got that the square root of 4096 is 64 and of 100 is 10.

___..

So,

$\sqrt{40.96} = \sqrt{ \frac{4096}{100} } = \frac{ \sqrt{4096} }{ \sqrt{100} }$

$= \frac{64}{10} = 6.4 \: ans...$

Hence, square root of 40.96 is 6.4.

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