Add or subtract as indicated and simplify.63y4+23y4−53y46\sqrt[4]{3y}+2\sqrt[4]{3y}-5\sqrt[4]{3y}

3 3 y 4 3\sqrt[4]{3y} 3 4 3 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">

Add or subtract as indicated and simplify. 6 3 y 4 + 2 3 y 4 − 5 3 y 4 6\sqrt[4]{3y}+2\sqrt[4]{3y}-5\sqrt[4]{3y}

we're asked to add or subtract as indicated and simplify. We're given here six times the fourth root of three y, plus two times the fourth root of three y, minus five times the fourth root of three y. Now these are all like radicals because they have the same index of four and the same radicand of three y. So I can go ahead and add or subtract by just looking at those coefficients. I have six plus two minus five. Six plus two gives me eight minus five gives me three. So this becomes three times the fourth root of three y, having added and subtracted those like radicals. Let me know if you have questions and I'll see you in the next one.

Add or subtract as indicated and simplify. 6 3 y 4 + 2 3 y 4 − 5 3 y 4 6\sqrt[4]{3y}+2\sqrt[4]{3y}-5\sqrt[4]{3y}

3 3 y 4 3\sqrt[4]{3y} 3 4 3 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">

5 3 y 4 5\sqrt[4]{3y} 5 4 3 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">

3 y 4 \sqrt[4]{3y} 4 3 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">

3 6 y 4 3\sqrt[4]{6y} 3 4 6 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

Adding and Subtracting Radicals

Intermediate Algebra

9. Roots, Radicals, and Complex Numbers

Adding and Subtracting Radicals

Struggling with Intermediate Algebra?

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Multiple Choice

Add or subtract as indicated and simplify.
$6 \sqrt[4]{3 y} + 2 \sqrt[4]{3 y} - 5 \sqrt[4]{3 y}$

$3\sqrt[4]{3y}$

$5\sqrt[4]{3y}$

$\sqrt[4]{3y}$

$3\sqrt[4]{6y}$

Verified step by step guidance

Identify the like terms in the expression. Here, all terms have the same radical part, which is the fourth root of $3y$, written as $\sqrt[4]{3y}$.

Since the radical parts are the same, you can combine the coefficients (the numbers in front of the radicals) by addition and subtraction.

Write the expression by factoring out the common radical: $6\sqrt[4]{3y} + 2\sqrt[4]{3y} - 5\sqrt[4]{3y} = (6 + 2 - 5)\sqrt[4]{3y}$.

Add and subtract the coefficients inside the parentheses: calculate $6 + 2 - 5$ to find the new coefficient.

Write the simplified expression as the product of the resulting coefficient and the common radical $\sqrt[4]{3y}$.

3:50m

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