Use the quotient rule to divide, then simplify. 144 16 \frac{\sqrt{144}}{\sqrt{16}}

we're asked to use the quotient rule to divide and then simplify. Now I have here the square root of one forty four over the square root of 16. So looking at this, these are already both perfect squares. So I could go ahead and just do these square roots to get here the square root of one forty four as 12 and the square root of 16 as four. So that's 12 divided by four, which is three, and that's my solution. Now there's another way that I could have come to this value because I could go ahead and use my quotient rule to rewrite this as the square root of one forty four divided by 16. Now one forty four divided by 16 is nine. So this is just the square root of nine, which we know is three. So we can see here that we could have used the quotient rule if we recognized that division. Or if you see two perfect squares and you just wanna do it that way, you'll still get the same solution. I'll see you in the next one.

Use the quotient rule to divide, then simplify. 144 16 \frac{\sqrt{144}}{\sqrt{16}}

3 \sqrt3 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">

6 \sqrt6 6 <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 divide, then simplify.
$\frac{\sqrt{144}}{\sqrt{16}}$

$6$

$3$

$\sqrt3$

$\sqrt6$

Verified step by step guidance

Recognize that the problem asks you to divide two square roots: $\frac{\sqrt{144}}{\sqrt{16}}$.

Apply the quotient rule for square roots, which states that $\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}$. So rewrite the expression as $\sqrt{\frac{144}{16}}$.

Simplify the fraction inside the square root by dividing 144 by 16, resulting in $\sqrt{9}$.

Evaluate the square root of 9, which is a perfect square, to simplify the expression further.

Write the simplified result as the final answer.

5:53m

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Use the quotient rule to divide, then simplify.14416\frac{\sqrt{144}}{\sqrt{16}}

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Use the quotient rule to divide, then simplify.
$\frac{\sqrt{144}}{\sqrt{16}}$