assuming x and y are both positive, write the following expression in simplest radical form. 5√(24x²y⁶)

Question

Accepted Answer

# Explanation:
## Step1: Factor the radicand
Factor $24x^{2}y^{6}$ into perfect squares and other factors: $24x^{2}y^{6}=4\times6\times x^{2}\times(y^{3})^{2}$, where $4 = 2^{2}$, $x^{2}$ and $(y^{3})^{2}$ are perfect squares.
## Step2: Simplify the square root
Using the property $\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}$ ($a\geq0,b\geq0$) and $\sqrt{a^{2}} = a$ ($a\geq0$):
$$
\begin{align*}
\sqrt{24x^{2}y^{6}}&=\sqrt{4\times6\times x^{2}\times(y^{3})^{2}}\
&=\sqrt{4}\times\sqrt{6}\times\sqrt{x^{2}}\times\sqrt{(y^{3})^{2}}\
&= 2\times\sqrt{6}\times x\times y^{3}\
&= 2xy^{3}\sqrt{6}
\end{align*}
$$
## Step3: Multiply by the coefficient outside the radical
Multiply $5$ with the simplified radical: $5\times2xy^{3}\sqrt{6}=10xy^{3}\sqrt{6}$

# Answer: $10xy^{3}\sqrt{6}$

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QUESTION IMAGE

Question

Explanation:

Step1: Factor the radicand

Step2: Simplify the square root

Step3: Multiply by the coefficient outside the radical

Answer: