Question

assuming x and y are both positive, write the following expression in simplest radical form.

3y³√(180x⁵y⁶)

Explanation:

Step1: Factor radicand into squares

$\sqrt{180x^5y^6} = \sqrt{36 \times 5 \times x^4 \times x \times y^6}$

Step2: Simplify the square root

$\sqrt{36x^4y^6 \times 5x} = 6x^2y^3\sqrt{5x}$

Step3: Multiply with outside term

$3y^3 \times 6x^2y^3\sqrt{5x}$

Step4: Combine like terms

$18x^2y^{3+3}\sqrt{5x} = 18x^2y^6\sqrt{5x}$

Answer:

$18x^2y^6\sqrt{5x}$