Which of the following is correct? (i) sqrt7 + sqrt2 > sqrt6 + sqrt3 (ii) sqrt7 + √(2) sqrt6 + sqrt3 (iii) sqrt7 + sqrt2 = sqrt6 + sqrt3

Which of the following is correct? (i) sqrt7 + sqrt2 >…

Which of the following is correct?

(i) $\sqrt7$ + $\sqrt2$ > $\sqrt6$ + $\sqrt3$

(ii) $\sqrt7$ + $\sqrt 2$ < $\sqrt6$ + $\sqrt3$

(iii) $\sqrt7$ + $\sqrt2$ = $\sqrt6$ + $\sqrt3$

Show answer & explanation

Correct answer: B

Explanation

The correct answer is option 2 i.e. (ii).

(√7 + √2)² = 7 + 2 + 2√14 = 9 + 2√14

(√6 + √3)² = 6 + 3 + 2√18 = 9 + 2√18

Since √18 > √14 then √7 + √2 < √6 + √3