Use the product rule to multiply the following.5x⋅7y\sqrt{5x}\cdot\sqrt{7y}

35 x y \sqrt{35xy} 35 x y <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 product rule to multiply the following. 5 x ⋅ 7 y \sqrt{5x}\cdot\sqrt{7y}

we're asked to use the product rule to multiply the following. We have the square root of five X times the square root of seven Y. So now we're throwing some variables into the mix, but we can still use our product rule in the same way. In order to condense these two square roots being multiplied into one, I wanna do that multiplication underneath one radical. So that makes this the square root of five x times seven y. Now we can do some further simplification here by going ahead and multiplying those constants five times seven in order to get us 35. So this becomes the square root of 35 x y. And this is my solution here, having used the product rule to perform that multiplication. I'll see you in the next one.

Use the product rule to multiply the following. 5 x ⋅ 7 y \sqrt{5x}\cdot\sqrt{7y}

35 x y \sqrt{35xy} 35 x y <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">

12 x 2 y 2 \sqrt{12x^2y^2} 12 x 2 y 2 <path d="M263,681c0.7,0,18,39.7,52,119 c34,79.3,68.167,158.7,102.5,238c34.3,79.3,51.8,119.3,52.5,120 c340,-704.7,510.7,-1060.3,512,-1067 l0 -0 c4.7,-7.3,11,-11,19,-11 H40000v40H1012.3 s-271.3,567,-271.3,567c-38.7,80.7,-84,175,-136,283c-52,108,-89.167,185.3,-111.5,232 c-22.3,46.7,-33.8,70.3,-34.5,71c-4.7,4.7,-12.3,7,-23,7s-12,-1,-12,-1 s-109,-253,-109,-253c-72.7,-168,-109.3,-252,-110,-252c-10.7,8,-22,16.7,-34,26 c-22,17.3,-33.3,26,-34,26s-26,-26,-26,-26s76,-59,76,-59s76,-60,76,-60z M1001 80h400000v40h-400000z">

12 x y \sqrt{12xy} 12 x y <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 product rule to multiply the following.
$\sqrt{5 x} \cdot \sqrt{7 y}$

$\sqrt{35xy}$

$35xy$

$\sqrt{12x^2y^2}$

$\sqrt{12xy}$

Verified step by step guidance

Recall the product rule for square roots: $\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}$. This means you can multiply the expressions inside the square roots together under a single square root.

Identify the expressions inside each square root: the first is \$5x$ and the second is $7y$.

Multiply the expressions inside the square roots: \$5x \times 7y = 35xy$.

Rewrite the product of the square roots as a single square root containing the product: $\sqrt{5x} \cdot \sqrt{7y} = \sqrt{35xy}$.

This expression $\sqrt{35xy}$ is the simplified product using the product rule for square roots.

5:53m

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