SSC Quantitative Aptitude Basic Calculations Question Bank Square and Cube Root (II)

If \[a=64\] and \[b=289,\] then the value of \[{{\left( \sqrt{\sqrt{a}+\sqrt{b}}-\sqrt{\sqrt{b}-\sqrt{a}} \right)}^{\frac{1}{2}}}\] is [SSC CGL Tier II, 2014]

A) \[{{2}^{\frac{1}{2}}}\]

B) 2

C) 4

D) \[-\,2\]

Correct Answer: A

Solution :

[a] \[a=64,\]\[b=289;\]\[{{(\sqrt{\sqrt{a}+\sqrt{b}}-\sqrt{\sqrt{b}-\sqrt{a}})}^{{\scriptstyle{}^{1}/{}_{2}}}}\] Putting the value of a and b \[{{\left( \sqrt{\sqrt{64}+\sqrt{289}}-\sqrt{\sqrt{289}-\sqrt{64}} \right)}^{\frac{1}{2}}}\] \[{{(\sqrt{8+17}-\sqrt{17-8})}^{{\scriptstyle{}^{1}/{}_{2}}}},\] \[{{(\sqrt{25}-\sqrt{9})}^{{\scriptstyle{}^{1}/{}_{2}}}}\,{{(5-3)}^{{\scriptstyle{}^{1}/{}_{2}}}}\] \[\Rightarrow \] \[{{(2)}^{{\scriptstyle{}^{1}/{}_{2}}}}\]

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SSC Quantitative Aptitude Basic Calculations Question Bank Square and Cube Root (II)

question_answer If \[a=64\] and \[b=289,\] then the value of \[{{\left( \sqrt{\sqrt{a}+\sqrt{b}}-\sqrt{\sqrt{b}-\sqrt{a}} \right)}^{\frac{1}{2}}}\] is [SSC CGL Tier II, 2014] A) \[{{2}^{\frac{1}{2}}}\] B) 2 C) 4 D) \[-\,2\]

If \[a=64\] and \[b=289,\] then the value of \[{{\left( \sqrt{\sqrt{a}+\sqrt{b}}-\sqrt{\sqrt{b}-\sqrt{a}} \right)}^{\frac{1}{2}}}\] is [SSC CGL Tier II, 2014]

A) \[{{2}^{\frac{1}{2}}}\]

B) 2

C) 4

D) \[-\,2\]