Prove that -1-4-0-01-1-2-272-3-3-2

To Prove: √(1/4)+(0.01)^ 1/2 (27)^2/3=3/2On simplifying LHS, we get=√(1/2^2)+(0.01× 100/1× 100)^ 1/2 (3^3)^2/30ex0ex=1/2+(1/100)^ 1/2 (3)^3×2/3Using, a^ n=1/a^n ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard IX

Mathematics

Property 1

Prove that √1...

Question

Prove that $\sqrt{\frac{1}{4}} + (0.01)^{- \frac{1}{2}} - (27)^{\frac{2}{3}} = \frac{3}{2}$

Open in App

Solution

To Prove: $\sqrt{\frac{1}{4}} + (0.01)^{- \frac{1}{2}} - (27)^{\frac{2}{3}} = \frac{3}{2}$
On simplifying LHS, we get
$= \sqrt{\frac{1}{2^{2}}} + {(\frac{0.01 \times 100}{1 \times 100})}^{- \frac{1}{2}} - {(3^{3})}^{\frac{2}{3}} = \frac{1}{2} + {(\frac{1}{100})}^{- \frac{1}{2}} - {(3)}^{3 \times \frac{2}{3}}$
Using, $a^{- n} = \frac{1}{a^{n}}$
$= \frac{1}{2} + 100^{\frac{1}{2}} - 3^{2}$
$= \frac{1}{2} + 10^{2 \times \frac{1}{2}} - 3^{2} = \frac{1}{2} + 10 - 3^{2}$
Simplify the above lines,
$= \frac{1}{2} + 10 - 9 = \frac{1 + 20 - 18}{2} = \frac{3}{2}$
Hence proved.

Suggest Corrections

Similar questions

Simplify $:$ $($ $\frac{3}{4}$ $\div$ $\frac{1}{2}$ $-$ $\frac{1}{3}$ $)$ $\times$ $\frac{6}{7}$

Simplify $:$ $\frac{2}{5}$ of $\frac{3}{7}$ $-$ $\frac{1}{14}$ $+$ $\frac{3}{7}$ of $\frac{3}{5}$

Simplify $:$ $\frac{3}{4}$ $\div$ $($ $\frac{1}{6}$ $\div$ $\frac{1}{2}$ $)$

Simplify $:$ $3$ $\frac{2}{4}$ $\div$ $($ $3$ $-$ $\frac{1}{4}$ $)$ $+$ $($ $\frac{2}{5}$ $\div$ $1$ $\frac{1}{5}$ $)$

Write $=$ or $\neq$ in the place holder.
$\frac{1}{8}$ $□$ $\frac{3}{4}$

Join BYJU'S Learning Program

Prove that 14+(0.01)-12-(27)23=32

To Prove: 14+(0.01)-12-(27)23=32On simplifying LHS, we get=122+0.01×1001×100-12-3323=12+1100-12-(3)3×23Using, a-n=1an=12+10012-32 =12+102×12-32=12+10-32Simplify the above lines,=12+10-9=1+20-182=32Hence proved.

Prove that $\sqrt{\frac{1}{4}} + (0.01)^{- \frac{1}{2}} - (27)^{\frac{2}{3}} = \frac{3}{2}$