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, Radicals, and Complex Numbers

Simplifying Radical Expressions

Intermediate Algebra

9. Roots, Radicals, and Complex Numbers

Simplifying Radical Expressions

Struggling with Intermediate 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

Recognize that the expression to simplify is $\sqrt{\frac{2}{81}}$, which is the square root of a fraction.

Recall the property of square roots that $\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$. Apply this to rewrite the expression as $\frac{\sqrt{2}}{\sqrt{81}}$.

Evaluate the square root in the denominator: since \$81$ is a perfect square, $\sqrt{81}$ simplifies to $9$.

Rewrite the expression as $\frac{\sqrt{2}}{9}$ after simplifying the denominator.

Confirm that the expression is simplified because the numerator contains an irrational number $\sqrt{2}$ and the denominator is a rational number \$9$, so no further simplification is possible.

5:53m

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