Question

The value of $\sqrt{99}$up to three decimals is-

• A. 9.949
• B. 9.958
• C. 9.948
• D. None of these

Answer 1

Answer: (A)

9.949

Answer 2

(99)^1/2 = (100 –1)^1/2

= 10 $\left( 1 - \frac{1}{10^{2}} \right)^{1/2}$

=10$\left\lbrack 1 - \frac{1}{2}.\frac{1}{10^{2}} + \frac{(1/2)(1/2 - 1)}{21}\left( - \frac{1}{10^{2}} \right)^{2} + ........ \right\rbrack$

= 10 [1 – 0.005 –0.0000125 +……….]

= 10[0.9949 …….]

= 9.949