Question

how to find the square root of 306.25

Answer 1

Answer:

The square root of 306.25 is 17.5

Step-by-step explanation:

I have found the square root by factorization method

$\bf\sqrt{306.25}$

$=\sqrt{\frac{30625}{100}}$

$=\sqrt{\frac{6125*5}{10*10}}$

$=\sqrt{\frac{1225*5*5}{10*10}}$

$=\sqrt{\frac{245*5*5*5}{10*10}}$

$=\sqrt{\frac{49*5*5*5*5}{10*10}}$

$=\sqrt{\frac{7*7*5*5*5*5}{10*10}}$

$=\frac{7*5*5}{10}$

$=\frac{175}{10}$

$=17.5$

$\implies\boxed{\bf\sqrt{306.25}=17.5}$

Answer 2

Answer:

The square root of 306.25 is 17.5

Step-by-step explanation:

I have found the square root by factorization method

\bf\sqrt{306.25}

306.25

=\sqrt{\frac{30625}{100}}=

100

30625

=\sqrt{\frac{6125*5}{10*10}}=

10∗10

6125∗5

=\sqrt{\frac{1225*5*5}{10*10}}=

10∗10

1225∗5∗5

=\sqrt{\frac{245*5*5*5}{10*10}}=

10∗10

245∗5∗5∗5

=\sqrt{\frac{49*5*5*5*5}{10*10}}=

10∗10

49∗5∗5∗5∗5

=\sqrt{\frac{7*7*5*5*5*5}{10*10}}=

10∗10

7∗7∗5∗5∗5∗5

=\frac{7*5*5}{10}=

10

7∗5∗5

=\frac{175}{10}=

10

175

=17.5=17.5

\implies\boxed{\bf\sqrt{306.25}=17.5}⟹

306.25

=17.5

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