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Parin Sir > Quantitative Aptitude (Maths) > Surds & Indices > Examples > Examples

Examples

May 30, 2020
Category: Examples

(1) What is the value of $\left (\frac{243}{32} \right )^{\frac{-4}{5}}$ ?

Soln. $\left (\frac{243}{32} \right )^{\frac{-4}{5}}$ = $\left (\frac{32}{243} \right )^{\frac{4}{5}}$ = $\left (\frac{2^{5}}{3^{5}} \right )^{\frac{4}{5}}$ = $\frac{2^{4}}{3^{4}}$ = $\frac{16}{81}$

(2) Convert $3\sqrt{5}$ into a pure surd.

Soln. $3\sqrt{5}$ = $\sqrt{3^{2}\times5}$ = $\sqrt{45}$

(3) Find the value of $\sqrt{98}$ + $\sqrt{50}$

Soln. $\sqrt{98}$ + $\sqrt{50}$ = $\sqrt{49\times 2}$ + $\sqrt{25\times 2}$ = 7 $\sqrt{2}$ + 5 $\sqrt{2}$ = 12 $\sqrt{2}$

(4) Which is greater $3\sqrt{10}$ or $4\sqrt{15}$ ?

Soln. Since L.C.M. of 3 and 4 is 12, we will take rest to 12 on both the sides.

$\left (\sqrt[3]{10} \right )^{12}$ = $10^{4}$ = 10000 $\left (\sqrt[4]{15} \right )^{12}$ = $15^{3}$ = 3375

Since 10000 > 3375, $\therefore \sqrt[3]{10} > \sqrt[4]{15}$

(5) If $\left (\frac{1}{1000} \right ) ^{\frac{-1}{3}}$ = x, what is the value of x ?

Soln. x = $\left (\frac{1}{1000} \right ) ^{\frac{-1}{3}}$ = $\left (1000 \right ) ^{\frac{1}{3}}$ = 10

(6) Reduce $\frac{3+\sqrt{2}}{5\sqrt{2}+7}$ to decimal fraction.

Soln. $\frac{3+\sqrt{2}}{5\sqrt{2}+7}$ = $\frac{3+\sqrt{2}}{5\sqrt{2}+7} \times \frac{5\sqrt{2}-7}{5\sqrt{2}+7}$ = $\frac{15\sqrt{2}-21+10-7\sqrt{2}}{50-49}$