Use the quotient rule to simplify.t83\sqrt[3]{\frac{t}{8}}

t 3 2 \frac{\sqrt[3]{t}}{2} 2 3 t <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. t 8 3 \sqrt[3]{\frac{t}{8}}

we're asked to use the quotient rule to simplify. We have here the cube root of a t over eight. Remember, we can use the quotient rule for nth roots just like we do square roots. So I can split this into the quotient of two cube roots. So this is the cube root of t over the cube root of eight. Now eight is a perfect cube. So the cube root of eight is two. So this is gonna give me here the cube root of t over two. And this is my simplified solution. Let me know if you have questions, and I'll see you in the next one.

Use the quotient rule to simplify. t 8 3 \sqrt[3]{\frac{t}{8}}

t 3 2 \frac{\sqrt[3]{t}}{2} 2 3 t <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">

t 2 \frac{\sqrt{t}}{2} 2 t <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">

t 8 \frac{\sqrt{t}}{8} 8 t <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.
$\sqrt[3]{\frac{t}{8}}$

$\frac{\sqrt{t}}{2}$

$\frac{t}{2}$

$\frac{\sqrt{t}}{8}$

$\frac{\sqrt[3]{t}}{2}$

Verified step by step guidance

Recognize that the expression $ \sqrt[3]{\frac{t}{8}} $ is a cube root of a fraction, which can be rewritten using the property of radicals: $ \sqrt[3]{\frac{a}{b}} = \frac{\sqrt[3]{a}}{\sqrt[3]{b}} $.

Apply this property to rewrite the expression as $ \frac{\sqrt[3]{t}}{\sqrt[3]{8}} $.

Recall that $ \sqrt[3]{8} $ is the cube root of 8, which simplifies to a number since 8 is a perfect cube.

Replace $ \sqrt[3]{8} $ with its simplified value to get $ \frac{\sqrt[3]{t}}{\text{simplified value}} $.

Write the final simplified expression as a fraction with $ \sqrt[3]{t} $ in the numerator and the simplified cube root of 8 in the denominator.

5:53m

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