Use the quotient rule to simplify. x 2 36 \sqrt{\frac{x^2}{36}}

we're asked to use the quotient rule to simplify. And we have here the square root of x squared over 36. So using the quotient rule, I can rewrite this as the square root of x squared over the square root of 36. This square root and square will cancel on the top, leaving me with just x. Then in my denominator, the square root of 36, that is a perfect square. That's going to give me just six. So this is my simplified solution, x over six. Let Let us know if you have any questions, and let's keep going.

Use the quotient rule to simplify. x 2 36 \sqrt{\frac{x^2}{36}}

x 36 \frac{\sqrt{x}}{36} 36 x <path d="M95,702 c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14 c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54 c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10 s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429 c69,-144,104.5,-217.7,106.5,-221 l0 -0 c5.3,-9.3,12,-14,20,-14 H400000v40H845.2724 s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7 c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z M834 80h400000v40h-400000z">

x 6 \frac{\sqrt{x}}{6} 6 x <path d="M95,702 c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14 c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54 c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10 s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429 c69,-144,104.5,-217.7,106.5,-221 l0 -0 c5.3,-9.3,12,-14,20,-14 H400000v40H845.2724 s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7 c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z M834 80h400000v40h-400000z">

9. Roots and Radicals

Simplifying Radical Expressions

Beginning Algebra

9. Roots and Radicals

Simplifying Radical Expressions

Struggling with Beginning Algebra?

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Multiple Choice

Use the quotient rule to simplify.
$\sqrt{\frac{x^{2}}{36}}$

$\frac{\sqrt{x}}{36}$

$\frac{x}{6}$

$\frac{\sqrt{x}}{6}$

$\frac{x^2}{6}$

Verified step by step guidance

Start with the expression under the square root: $\sqrt{\frac{x^2}{36}}$.

Recall the property of square roots that $\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$. Apply this to rewrite the expression as $\frac{\sqrt{x^2}}{\sqrt{36}}$.

Simplify the square roots separately: $\sqrt{x^2}$ simplifies to $|x|$ (the absolute value of $x$), and $\sqrt{36}$ simplifies to \$6$.

Rewrite the expression as $\frac{|x|}{6}$.

If the context allows (for example, if $x$ is nonnegative), you can simplify $|x|$ to $x$, resulting in $\frac{x}{6}$.

5:28m

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Use the quotient rule to simplify.x236\sqrt{\frac{x^2}{36}}

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Use the quotient rule to simplify.
$\sqrt{\frac{x^{2}}{36}}$