Question:
\[
\frac{5^{\frac{3}{2}} - 2^{\frac{3}{2}}}{\sqrt{5}-\sqrt{2}} + \frac{5^{\frac{3}{2}} + 2^{\frac{3}{2}}}{\sqrt{5}+\sqrt{2}}
\]
\[
\frac{5^{\frac{3}{2}} - 2^{\frac{3}{2}}}{\sqrt{5}-\sqrt{2}} + \frac{5^{\frac{3}{2}} + 2^{\frac{3}{2}}}{\sqrt{5}+\sqrt{2}}
\]
Show Hint
Use conjugate-based identities to simplify radical fractions quickly.
Updated On: Apr 15, 2026
- 7
- 14
- 12
- 8
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Concept:
Use identity:
\[
a^{3/2} = a\sqrt{a}
\]
Step 1: Rewrite.
\[ 5^{3/2} = 5\sqrt{5}, \quad 2^{3/2} = 2\sqrt{2} \]
Step 2: Substitute.
\[ \frac{5\sqrt{5} - 2\sqrt{2}}{\sqrt{5}-\sqrt{2}} = 5 + 2 = 7 \] \[ \frac{5\sqrt{5} + 2\sqrt{2}}{\sqrt{5}+\sqrt{2}} = 5 + 2 = 7 \]
Step 3: Final.
\[ 7 + 7 = 14 \]
Step 1: Rewrite.
\[ 5^{3/2} = 5\sqrt{5}, \quad 2^{3/2} = 2\sqrt{2} \]
Step 2: Substitute.
\[ \frac{5\sqrt{5} - 2\sqrt{2}}{\sqrt{5}-\sqrt{2}} = 5 + 2 = 7 \] \[ \frac{5\sqrt{5} + 2\sqrt{2}}{\sqrt{5}+\sqrt{2}} = 5 + 2 = 7 \]
Step 3: Final.
\[ 7 + 7 = 14 \]
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