Use the quotient rule to simplify.281\sqrt{\frac{2}{81}}

2 9 \frac{\sqrt2}{9} 9 2 <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">

Use the quotient rule to simplify. 2 81 \sqrt{\frac{2}{81}}

we're asked to use the quotient rule to simplify. We have here the square root of two over 81. So using the quotient rule here, I can split this into a quotient of two square roots. So that's the square root of two over the square root of 81. Now square root of 81 is nine. That's a perfect square, so that makes this the square root of two over nine. Now I can't further simplify this root two, so this is actually my final answer here root two over nine. It's okay if when using the quotient rule it doesn't always work out to be a perfect square. We can see that this is still a simplification from what we started with: root two over nine compared to the square root of two over 81. What we're really trying to do with any of these radical rules is pull out any perfect squares that we can, which is exactly what we did using the quotient rule. I'll see you in the next one.

Use the quotient rule to simplify. 2 81 \sqrt{\frac{2}{81}}

2 9 \frac{\sqrt2}{9} 9 2 <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">

2 81 \frac{\sqrt2}{81} 81 2 <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.
$\sqrt{\frac{2}{81}}$

$\frac{\sqrt2}{81}$

$\frac29$

$\frac{2}{81}$

$\frac{\sqrt2}{9}$

Verified step by step guidance

Start with the expression under the square root: $\sqrt{\frac{2}{81}}$.

Recall the property of square roots that allows you to separate the square root of a fraction into the fraction of square roots: $\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$.

Apply this property to rewrite the expression as $\frac{\sqrt{2}}{\sqrt{81}}$.

Simplify the denominator by recognizing that $\sqrt{81}$ is a perfect square, so $\sqrt{81} = 9$.

Rewrite the expression as $\frac{\sqrt{2}}{9}$, which is the simplified form.

5:28m

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