Problem 18

Simplify each expression. $$\sqrt{192}$$

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Problem 17

Simplify each expression.
$$\frac{18}{\sqrt{162}}$$

Answer

$\sqrt{2}$


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Video Transcript

to simplify this expression, we have to see if there's a square toe 1 62 1st So if you type it in your calculator, you get a decimal and we don't wanna have any decimals. So the next thing we have to do is see if there's a way we can break down the radical. And by doing that, we're going to see if there is a perfect square that can divide 1 62 So start dividing 1 62 by four by nine 16 25 etcetera Those air all the perfect squares, you end up figuring out that 1 62 can be divided evenly by 81. So what you end up with is a square to 81 times a squared of two. Since 81 times two is 1 62 then the skirt 81 is just nine. So you end up with nine. Brad, too. So now we have 18 over nine. Rad, too, but we don't want to leave her answer with a radical in the denominator. So in order to get the radical out of the denominator, we do something called Rationalizing the denominator. So we know that if we multiply squared of to buy the squared of two. We're left with just two. But whatever you do to the bottom, you have to do to the top. So if we multiply the top and bottom by the squared of two, we end up getting 18 times, escorted to over nine times. Rad. Two times Rad two is just too. So we have 18 rad two over 18. Now the 18 cancel out, and our final answer is just the square root of two.

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