1Cademy - Simplifying $$\sqrt{121a^6b^8}$$

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Square Roots of Variable Expressions

Example

Simplifying $\sqrt{121a^6b^8}$

Simplify a square root whose radicand is a product of a numerical perfect square and two variables raised to higher even powers.

$\sqrt{121a^6b^8}$

Identify the expression whose square equals the radicand. Since $(11a^3b^4)^2 = 121a^6b^8$ , the result is:

$\sqrt{121a^6b^8} = 11a^3b^4$

Each part of the radicand is handled separately: the coefficient $121$ is a perfect square ( $11^2 = 121$ ); the exponent $6$ on $a$ is even, so halving it gives $a^3$ ; and the exponent $8$ on $b$ is even, so halving it gives $b^4$ . Combining these yields $11a^3b^4$ . This example extends the two-variable technique to cases where the variables have exponents greater than $2$ , showing that the halving procedure applies to each variable independently no matter how large its even exponent.

Updated 2026-04-21

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OpenStax Elementary Algebra

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