Keerthana
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Which value among 11+5,14+2,8sqrt{11}+sqrt{5}, sqrt{14}+sqrt{2}, sqrt{8} +8+sqrt{8} is the largest ?

a

All are equal

b

8+8sqrt{8}+sqrt{8}

c

14+2sqrt{14}+sqrt{2}

d

11+5sqrt{11}+sqrt{5}

Answer : Option B
Explanation :

(11+5)2=11+5+255=16+255(sqrt{11}+sqrt{5})^{2}=11+5+2 sqrt{55}=16+2 sqrt{55}

(14+2)2=14+2+228=16+228(sqrt{14}+sqrt{2})^{2}=14+2+2 sqrt{28}=16+2 sqrt{28}

(8+8)2=8+8+264=16+264(sqrt{8}+sqrt{8})^{2}=8+8+2 sqrt{64}=16+2 sqrt{64}

16+228<16+255<16+26416+2 sqrt{28}<16+2 sqrt{55}<16+2 sqrt{64}

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