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Which of the following is correct?(i) √7 + √2 > √6 + √3(ii) √7 + √2 < √6 + √3(iii) √7 + √2 = √6 + √3
Question

Which of the following is correct?
(i) √7 + √2 > √6 + √3
(ii) √7 + √2 < √6 + √3
(iii) √7 + √2 = √6 + √3

A.

(i)

B.

(ii)

C.

(iii)

D.

(i), (ii) and (iii)

Correct option is B

Given:
√7 + √2 and √6 + √3
Formula Used:
If a > 0 and b > 0, then a > b ⇔ a² > b²
Solution:
(√7 + √2)² = 7 + 2 + 2√14 = 9 + 2√14
(√6 + √3)² = 6 + 3 + 2√18 = 9 + 2√18
Since √18 > √14,
9 + 2√18 > 9 + 2√14
Therefore, √6 + √3 > √7 + √2
Hence, statement (ii) is correct.


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