Question

write the expression so the radicand has no perfect squares other than 1.
-26\sqrt{75x^{11}}

-26\sqrt{75x^{11}} = \square
(type an exact answer, using radicals as needed.)

Explanation:

Step1: Factor radicand into perfect squares

$\sqrt{75x^{11}} = \sqrt{25 \times 3 \times x^{10} \times x}$

Step2: Separate perfect square factors

$= \sqrt{25} \times \sqrt{x^{10}} \times \sqrt{3x}$

Step3: Simplify perfect square roots

$= 5 \times x^5 \times \sqrt{3x}$

Step4: Multiply with the coefficient

$-26 \times 5x^5\sqrt{3x}$

Answer:

$-130x^5\sqrt{3x}$