Rough rule of thumb for square root

[user902]

Hello, I just wanted to check my understanding of square root for the GRE.

• If there is a numerical value inside a radical (eg √36 or √49) we just take positive rather than the abs.
• But if we put a variable (ie √(x sq) or √x) we consider every value of x that would be valid under the radical?

So tl:dr, number → take positive root
& expression with variables → consider each possibility, positive and negative?

[ganesh]

I think it would be abs value for both.

Can you check this example?

Roots and Negatives

@Tishi Note in Leaderboard’s example that \sqrt{14} is still positive. In the GRE, \sqrt{64} means |\sqrt{64}|, which is always 8. However, if an equation said that x^2=64, then we have the following: x=\sqrt{64} → x=|\sqrt{64}| → x=8 x=-\sqrt{64} → x=-|\sqrt{64}| → x=-8 Note that \sqrt{64} always equals 8.

Hopefully it clarifies when you should consider positive and negative roots.

[itisnihal]

If we would take sqrt(x^4), then, x can have negative values right?

[ganesh]

Nope. That would still be |x^2|