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Question Detail
\begin{aligned} \sqrt{8}^\frac{1}{3} \end{aligned}
- 2
- 4
- \begin{aligned} \sqrt{2} \end{aligned}
- 8
Answer: Option C
Explanation:
\begin{aligned}
= ((8)^\frac{1}{2})^\frac{1}{3} = 8^{(\frac{1}{2} \times \frac{1}{3})}
\end{aligned}
\begin{aligned}
= (8)^{\frac{1}{6}}
\end{aligned}
\begin{aligned}
= (2)^{3(\frac{1}{6})}
\end{aligned}
\begin{aligned}
= (2)^{\frac{1}{2}}
\end{aligned}
1. Find the value of
\begin{aligned} (10)^{150} \div (10)^{146} \end{aligned}
- 10
- 100
- 1000
- 10000
Answer: Option D
Explanation:
\begin{aligned}
= \frac{(10)^{150}}{(10)^{146}} = 10^4 = 10000
\end{aligned}
2. Find the value of,
\begin{aligned}
\frac{1}{216^{-\frac{2}{3}}}+\frac{1}{256^{-\frac{3}{4}}}+\frac{1}{32^{-\frac{1}{5}}}
\end{aligned}
- 100
- 101
- 102
- 103
Answer: Option C
3. \begin{aligned}
x = 3 + 2\sqrt{2}, \text{ then the value of }\\
(\sqrt{x} - \frac{1}{\sqrt{x}})
\end{aligned}
- 1
- 2
- 3
- 4
Answer: Option B
Explanation:
Clue:
\begin{aligned}
(\sqrt{x} - \frac{1}{\sqrt{x}})^2 = x + \frac{1}{x} - 2 \
\end{aligned}
Now put the value of x to calculate the answer :)
4. \begin{aligned} \sqrt{8}^\frac{1}{3} \end{aligned}
- 2
- 4
- \begin{aligned} \sqrt{2} \end{aligned}
- 8
Answer: Option C
Explanation:
\begin{aligned}
= ((8)^\frac{1}{2})^\frac{1}{3} = 8^{(\frac{1}{2} \times \frac{1}{3})}
\end{aligned}
\begin{aligned}
= (8)^{\frac{1}{6}}
\end{aligned}
\begin{aligned}
= (2)^{3(\frac{1}{6})}
\end{aligned}
\begin{aligned}
= (2)^{\frac{1}{2}}
\end{aligned}
5. \begin{aligned}
\left(25 \right)^{7.5} \times \left(5 \right)^{2.5} \div \left(125 \right)^{1.5} = 5^?
\end{aligned}
- 9.7
- 11.5
- 12
- 13
Answer: Option D
Explanation:
Lets assume,
\begin{aligned}
\left(25 \right)^{7.5} \times \left(5 \right)^{2.5} \div \left(125 \right)^{1.5} = 5^x \\
\text{then, } \frac{ \left( 5^2 \right)^{7.5} \times \left(5 \right)^{2.5} }{\left(5^3 \right)^{1.5} } = 5^x \\
=> \text{then, } \frac{ \left( 5^{15} \right) \times \left(5^{2.5} \right) }{\left(5^{4.5} \right) } = 5^x \\
=> 5^x = 5^{15 + 2.5 - 4.5} \\
=> 5^x = 5^{13} \\
\text{Hence, } x = 13
\end{aligned}
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