A) \[\left( 6+\sqrt{2} \right)\]
B) \[\left( 5+\sqrt{13} \right)\]
C) \[\left( \frac{\sqrt{75}+1}{\sqrt{2}} \right)\]
D) \[\left( 6+\sqrt{13} \right)\]
Correct Answer: C
Solution :
\[38+5\sqrt{3}=\frac{76+10\sqrt{3}}{2}\] \[=\frac{76+2\sqrt{75}}{2}=\frac{{{\left( \sqrt{75}+1 \right)}^{2}}}{{{\left( \sqrt{2} \right)}^{2}}}={{\left( \frac{\sqrt{75}+1}{\sqrt{2}} \right)}^{2}}\] \[\therefore \,\] Square root \[=\underline{\frac{\sqrt{\mathbf{75}}\mathbf{+1}}{\sqrt{\mathbf{2}}}}\]
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