QQuestionMathematics
QuestionMathematics
Which expression is equivalent to $\sqrt{B x^{2} y^{8}}$ ? Assume $x \geq 0$.
\begin{aligned}
& \text { ○ } x y^{2} \sqrt{B x^{3}} \\
& \text { ○ } 2 x^{3} y^{3} \sqrt{x y^{2}} \\
& \text { ○ } 2 x^{3} y^{4} \sqrt{2 x} \\
& \text { ○ } 4 x^{3} y^{4} \sqrt{x}
\end{aligned}
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Answer
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Step 1:: Identify the formula for simplifying a square root of a product.
The square root of a product is the product of the square roots of the factors: $$\sqrt{a b} = \sqrt{a} \sqrt{b}
Step 2:: Apply the formula to the given expression.
\sqrt{B x^{2} y^{8}} = \sqrt{B} \sqrt{x^{2}} \sqrt{y^{8}}
Step 3:: Simplify the exponents of y using the power rule: (a^{m})^{n} = a^{m n}.
\sqrt{B} \sqrt{x^{2}} \sqrt{(y^{4})^{2}}
Step 4:: Recall that \sqrt{a^{2}} = |a|.
Since $$x$$ is non-negative, we can simplify further.
\sqrt{B} \cdot |x| \cdot |y^{4}| = \sqrt{B} \cdot x \cdot y^{4}
Step 5:: Compare the simplified expression to the given answer choices.
However, since $$x$$ is non-negative, the absolute value is not needed, and the answer should be:
Final Answer
x y^{4} \sqrt{B x}
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