Simplify $\sqrt{-81x^4y^2}$

Key takeaway: Before simplifying a square root, check the sign of the radicand. A square root of a negative number is not real in the real-number system.

We look at the radicand:

$\sqrt{-81x^4y^2}$

Since $-81x^4y^2$ is negative whenever $x$ and $y$ are real numbers, the square root is not a real number.

Therefore the answer is

NOT REAL

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Pitfalls the pros know 👇 Do not try to simplify the factors first and ignore the negative sign. The presence of a negative radicand means the expression has no real value.

What if the problem changes? If the expression were $\sqrt{81x^4y^2}$, then it would simplify to $9x^2|y|$. The negative sign is what makes the original problem not real.

Tags: radicand, real number, square root