Question

Find the value of $\sqrt{3}0$ till the four places of decimal.

• A. $5.4778$
• B. $5.9991$
• C. $5.6281$
• D. $5.2223$

Answer 1

Answer: (A)

$5.4778$

${\left(30\right)}^{1/2}={(25+5)}^{1/2}$

$=(25{)}^{1/2}+\frac{1}{2}.(25{)}^{-1/2}.5+\frac{\frac{1}{2}\times \frac{-1}{2}}{2!}.{\left(25\right)}^{-3/2}.{\left(5\right)}^2+\frac{\frac{1}{2}\times \frac{-1}{2}\times \frac{-3}{2}}{3!}\times {\left(25\right)}^{-5/2}.{\left(5\right)}^3+......$

$=5+\frac{1}{2}\times \frac{1}{5}\times 5+\frac{-1}{8}\times \frac{1}{5^3}\times 5^2+\frac{1}{16}\times \frac{1}{5^5}\times 5^3......$

$=5+\frac{1}{2}-\frac{1}{40}+\frac{1}{400}-\frac{1}{3200}......$

$=5+0.5-0.025+0.0025-0.0003125$

$=5.4778125$

Further values will give more precise output,

Hence the answer is $5.4778$ approximately.