Use the quotient rule to divide, then simplify. 75 3 \frac{\sqrt{75}}{\sqrt3}

we're asked to use the quotient rule to divide and then simplify. We're given here the square root of 75 divided by the square root of three. Now neither of these are perfect squares, but let's see what happens when we use the quotient rule to put this division under one radical. This then becomes the square root of 75 divided by three. 75 divided by three is 25, so that makes this the square root of 25, a perfect square. So the square root of 25 is five, and having used the quotient rule to divide underneath one radical leads me to this much more simple solution. I'll see you in the next one.

Use the quotient rule to divide, then simplify. 75 3 \frac{\sqrt{75}}{\sqrt3}

3 5 3\sqrt5 3 5 <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">

5 \sqrt5 5 <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">

5 3 5\sqrt3 5 3 <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 divide, then simplify.
$\frac{\sqrt{75}}{\sqrt{3}}$

$5$

$3\sqrt5$

$\sqrt5$

$5\sqrt3$

Verified step by step guidance

Start with the given expression: $\frac{\sqrt{75}}{\sqrt{3}}$.

Use the quotient rule for radicals, which states that $\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}$. So rewrite the expression as $\sqrt{\frac{75}{3}}$.

Simplify the fraction inside the square root: $\frac{75}{3} = 25$, so the expression becomes $\sqrt{25}$.

Recognize that $\sqrt{25}$ is a perfect square, and can be simplified further.

Simplify $\sqrt{25}$ to its simplest form by finding the number whose square is 25.

5:28m

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Use the quotient rule to divide, then simplify.753\frac{\sqrt{75}}{\sqrt3}

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Use the quotient rule to divide, then simplify.
$\frac{\sqrt{75}}{\sqrt{3}}$