Which is greater, √(5) + √(3) or √(6) + √(2)?

Numerical Inequalities · Question 35 of 79

Question 35

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Which is greater, $\sqrt{5} + \sqrt{3}$ or $\sqrt{6} + \sqrt{2}$ ?

\sqrt{5} + \sqrt{3}

Correct answerYour answer

\sqrt{6} + \sqrt{2}

Correct answerYour answerThey are equalCorrect answerYour answerIt depends on roundingCorrect answerYour answer

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CorrectNot quiteAnswer A

Correct answer: A

Both are positive, so compare their squares: $8 + 2\sqrt{15}$ and $8 + 2\sqrt{12}$ .
$\sqrt{15} > \sqrt{12}$ , so $\sqrt{5} + \sqrt{3}$ is greater.

Worth noting

Both sums are of numbers adding to 8 under the roots; the closer the two numbers, the larger the sum of roots.

Ten questions from Numerical Inequalities, at your own pace.

Ten questions from Numerical Inequalities, at your own pace.