Square Root Inequality

Algebra Level 1

Which of the following is equivalent to:

$4 < \sqrt{x} < 9 \, ?$

0 < \sqrt{x} < 5

2 < x < 3

0 < x < 81

16 < x < 81

1 solution

Angela Fajardo
Nov 3, 2016

$\large \begin{matrix} 4 & < & \sqrt { x } & < & 9 \\ { 4 }^{ 2 } & < & { \sqrt { x } }^{ 2 } & < & { 9 }^{ 2 } \\ 16 & < & x & < & 81 \end{matrix}$

That works. In this case, because all terms are positive, we can square. But otherwise, we have to be careful with squaring inequalities with negative values.

Chung Kevin - 4 years, 7 months ago

Square Root Inequality

1 solution

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