Question

Conndentiality StatAdapt Web Service5 New TabMoodle-Bunker Hil.cSimplify. (Assume x > 0 and y>0.)✓ 48x58Step 1 of 1Factor the radicand into perfect square factors and factors that are not perfect square factors.Find the perfect square factors of 48x5y For variable factors, powers that are multiples of 2 are perfectsquare factors. Note that 48 can be rewritten as the product of 16 (a perfect square) and 3. Also, xs can berewritten as the product of 4 (a perfect square) and x. Finally, note that y8 is already a perfect square anddoes not need to be rewritten48x5y3 = ✓ (16)(3)(**)(x)(8)Use the product rule for square roots to write the radical expression as the product of perfect square factorsand factors that are not perfect squares. Then, take the square root of the perfect square factors.(16)(3)(**)(x)(y) = V(16x4y8) - (3x)3x√3xThus, the simplification process results in the following expression

Answer 1

Remember the product rule for square roots:

`\sqrt[]{a\cdot b}=\sqrt[]{a}\cdot\sqrt[]{b}`

Once the radicand has been rewritten as the product of perfect square factors and factors that are not perfect squares, use the product rule and take the square root of the perfect square factors:

`\begin{gathered} \sqrt[]{(16x^4y^8)(3x)}=\sqrt[]{16x^4y^8}\cdot\sqrt[]{3x} \\ =4x^2y^4\cdot\sqrt[]{3x} \end{gathered}`

Thus, the simplification process results in the following expression:

`4x^2y^4\cdot\sqrt[]{3x}`