Find the square root of the following decimal numbers.

Question

asked Sep 7, 2022 65.3k views

2 Answers

Syed Mohamed · Answer 1 · 2022-09-12T20:13:40+0000

Answer:

$\huge \boxed{ \tt i)1.6} \\ \huge \boxed{ \tt ii)4.3} \\ \huge \boxed{ \tt iii)8.3} \\ \huge \boxed{ \: \: \: \: \tt iv)9.2 \: \: \: }$

Explanation:

tips for finding square root by division method

Group the digits in pairs, starting with the digit in the units place
Think of the largest number whose square is equal to or just less than the first period. Take this number as the divisor and also as the quotient.
Subtract the product of the divisor and the quotient from the first period and bring down the next period to the right of the remainder.
the new divisor is obtained by taking two times the quotient and annexing with it a suitable digit which is also taken as the next digit of the quotient, chosen in such a way that the product of the new divisor and this digit is equal to or just less than the new dividend.
Repeat steps till all the periods have been taken up

tips for converting decimal to a fraction

solve the square roots using division method:

solve the square roots by converting decimals into fraction:

$\tt i) √(2.56) \\ \tt \sqrt{ (256)/(100) } \\ \tt \sqrt{ \frac{1 {6}^(2) }{ {10}^(2) } } \\ \tt(16)/(10) \\ \tt \: 1.6$

$\tt ii) √(18.49) \\ \tt \sqrt{ (1849)/(100) } \\ \tt\sqrt{ \frac{ {43}^(2) }{ {10}^(2) } } \\ \tt (43)/(10) \\ \tt 4.3$

$\tt iii) √( 68.89) \\ \tt \sqrt{ (6889)/(100) } \\ \tt \sqrt{ \frac{ {83}^(2) }{ {10}^(2) } } \\ \tt (83)/(10) \\ \tt 8.3$

$\tt iv) √(84.64) \\ \tt\sqrt{ (8464)/(100) } \\ \tt\sqrt{ \frac{ {92}^(2) }{ {10}^(2) } } \\ \tt (92)/(10) \\ \tt9.2$