saumya17lc wrote:

If x=5√−37

then which of the following must be true?

√−x>2

x>−2

x2<4

x3<−8

x4>32

GREPREP club question- Quant test 6 Question 11 of 20 ID: Q02-99

Just want to add few details in the explanation-

Points to remember- Odd roots have same signs

eg \(3\sqrt{-125}\) =-5 and \(3\sqrt{125}\) =5 Now back to question-

we know \(5\sqrt{32}\)=2 so \(5\sqrt{-37}\)≈2.1 ( it should be slightly greater than \(2^5\))

Now we can check with each option-

only option D fits the sol. because \((-2.1)^3\) < -8 so \(x^3\)<−8

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