Question

Find the square root of 40.96 by prime factorization method.​

Answer 1

Answer: Square root of 40.96 is 6.4

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Answer 2

Answer-

✴ Square root of 40.96 is 6.4 ✴.

Step-by-step explanation-

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

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

Prime factorization of 4096,

We get,

$4096 =<u> </u><u>\</u><u>u</u><u>n</u><u>d</u><u>e</u><u>r</u><u>l</u><u>i</u><u>n</u><u>e</u><u> </u><u>{</u><u>2 \times 2</u><u>}</u><u> </u>\times<u> </u><u> \underline</u><u>{</u><u>2 \times 2</u><u>}</u> \times <u> \underline</u><u> </u><u>{</u><u>2 \times 2</u><u>}</u><u> </u>\times <u> \underline</u><u>{</u><u>8 \times 8</u><u>}</u>$

( 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,

$100 = <u> \underline</u><u> </u><u>{</u><u>10 \times 10</u><u>}</u>$

$\sqrt{100 } = 10$

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

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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.