True or False: 9 + 16 \sqrt{9+16} 9 + 16 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z"> and 9 + 16 \sqrt9+\sqrt{16} 9 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z"> + 16 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z"> are equal.

Alright. So let's take a look at this problem here. So we're asked sort of a true or false question. Is the square root of 9 plus 16 all under one radical and square root of 9 plus square root of 16 different radicals, are those things equal to each other? Well, let's find out. If you have a square roots of 9 +16, that's all under the same radical. What ends up happening here is that you could basically treat this radical as like a parenthesis. You can do everything that's inside of the parenthesis or inside of the radical, and you can simplify before you take the square roots. So in other words, this really just becomes the square root of 25. We know that the square root of 25, the positive root, however, or is just is just 5. So that's what the square root of 9 +16 altogether is. So is that the same thing as square root of 9+thesquare root of 16? Well, what happens is square root of 9 +2square root of 16 is basically like saying 3+4, right? That's a perfect square, that's a perfect square, and this is actually just equal to 7. So notice how these two things are not equal to each other. Alright? So 1 is 5 and 1 is 7. So this is really really important. Again, this is why you can't actually just take 2 square roots and just sort of mash them together it's because that doesn't actually equal the same thing. This is equal to 5, but this expression is equal to 7. So it's actually false. So, this is false. Make sure that you don't do this. This is a big mistake, and you're gonna get the wrong answer. Alright? Thanks for watching.

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0. Fundamental Concepts of Algebra

Simplifying Radical Expressions

Precalculus

0. Fundamental Concepts of Algebra

Simplifying Radical Expressions

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Multiple Choice

True or False:
$\sqrt{9+16}$ and $\sqrt\)9+\(\sqrt{16}$ are equal.

True

False

Cannot be determined

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검증된 단계별 안내

First, let's clarify the expressions: The first expression is 9 + 16$\sqrt{9+16}$, and the second expression is 9 + 16$\sqrt{9}$ + $\sqrt{16}$.

For the first expression, 9 + 16$\sqrt{9+16}$, evaluate the term inside the square root: 9 + 16 = 25.

Now, substitute back into the expression: 9 + 16$\sqrt{25}$.

For the second expression, 9 + 16$\sqrt{9}$ + $\sqrt{16}$, evaluate each square root separately: $\sqrt{9}$ = 3 and $\sqrt{16}$ = 4.

Substitute these values back into the expression: 9 + 16(3) + 4. Compare the simplified forms of both expressions to determine if they are equal.

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Struggling with Precalculus?

True or False:9+16\(\sqrt{9+16}\)9+16 and 9+16\(\sqrt\)9+\(\sqrt{16}\)9+16 are equal.

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Simplifying Radical Expressions practice set

True or False:
$\sqrt{9+16}$ and $\sqrt\)9+\(\sqrt{16}$ are equal.