If a= 15+ 13- 12, b= 15- 13+ 12, c=- 15+ 13+ 12, which of the following is true?

Free Practice Question

PS · Problem Solving

605-655

Arithmetic

If $a=\sqrt{15}+\sqrt{13}-\sqrt{12}$ , $b=\sqrt{15}-\sqrt{13}+\sqrt{12}$ , $c=-\sqrt{15}+\sqrt{13}+\sqrt{12}$ , which of the following is true?

Correct answer marked below

a < c < b

a < b < c

c < b < a

Correct

c < a < b

b < a < c

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Comments

VatadeMay 21

These radicals are messy. I tried squaring a and b to compare, but got stuck. Is there a simpler way?

EbrahemMay 31

Maybe compare the differences? Like a-b = 2√13 - 2√12, which is positive, so a > b. Then compare b and c similarly.

SanjnaApr 17

I noticed that a and c are opposites except for the middle term. Does that help?

RockyApr 18

Yes! a-c = 2√15 - 2√13, which is positive, so a > c. Then with a > b and a > c, and comparing b and c...

PaoloAug 18

This was tricky but I got it by estimating the square roots. √15≈3.873, √13≈3.606, √12≈3.464. Then a≈4.015, b≈3.731, c≈3.195. So a>b>c.

What this question tests

Your fluency with the order of operations, fractions, decimals, and basic number sense — the foundation every quant question leans on.

Applying the order of operations out of sequence or rounding intermediate values before the final step.