Question

Find the square root of 56.25, without using long division method?

Answer 1

✓56.25=7.5
first we consider 25..so unit digit will be 5
and for 7²<56>8²
so 7.5 is the answer

Answer 2

The square root of 56.25 is 7.5

• Let us solve this one using prime factorization method
• $56.25 = \frac{5625}{100}$

• 5625 = 5 x 1125

                  = 5 x 5 x 225

                  = 5 x 5 x 5 x 45

                  = 5 x 5 x 5 x 5 x 9

                  = 5 x 5 x 5 x 5 x 3 x 3

                  = $5^{4}$ x $3^{2}$

• 100 = 10 x 10

               = $10^{2}$

• $\sqrt{56.25} = \sqrt{\frac{5625}{100} }$

                   $= \sqrt{\frac{5^{4}3^{2} }{10^{2} } }$

                   $= \frac{5^{2}3 }{10}$

                   $= \frac{75}{10}$

                   $=$ 7.5