Q11 of 81 Page 161

Let us write which one is greater of √15 + √3 and √10 + √8

1st value is √15 + √3


Its square is


(√15 + √3)2 = (√15)2 + (√3)2 + 2 × √15 × √3 = 15 + 3 + 2√45 = 18 + 2√45


2nd value is √10 + √8


Its square is


(√10 + √8)2 = (√10)2 + (√8)2 + 2 × √10 × √8 = 10 + 8 + 2√80 = 18 + 2√80


If 45<80


Then √45 < √80


Then 18 + √45 < 18 + √80


Then √(18 + √45) < √(18 + √80)


∴ √15 + √3 < √10 + √8


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