For each question, select the proper option from four options given, to make the statement true : (Final answer only)
If $(\sqrt{5}+3)^{2}=a+b \sqrt{5},$ then........
$a=14, b=6$
$a=8, b=3$
$a=14, b=3$
$a=8, b=6$
Simplify $: 2^{-3}+(0.01)^{-\frac{1}{2}}-(27)^{\frac{2}{3}}$
Simplify:
$(\frac{1}{27})^{\frac{-2}{3}}$
Simplify:
${{(625)^{-\frac{1}{2}}}^{-\frac{1}{4}}}^{2}$
Find the values of each of the following correct to three places of decimals, rationalising the denominator if needed and taking $\sqrt{2}=1.414$ $\sqrt{3}=1.732$ and $\sqrt{5}=2.236$
$\frac{\sqrt{10}-\sqrt{5}}{2}$
Find three different irrational numbers between the rational numbers $\frac{1}{3}$ and $\frac{7}{9}$.