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In $3-38$ write each expression in simplest form. Variables in the radicand with an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero.$$a \sqrt{45}+\sqrt{20 a^{2}}-5 \sqrt{2 a}$$

$5 \sqrt{5} a-5 \sqrt{2 a}$

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Chapter 3

REAL NUMBERS AND RADICALS

Section 4

Adding and Subtracting Radicals

Whole which of Numbers

Fractions and Mixed Numbers

Decimals

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we're being asked to simplify the given expression. So the first thing we need to do is simplify each of our radicals. So let's start with our first term. We have a times to square the 45. So the perfect square nine goes into 45 9 times. So I'm gonna rewrite this as a times the square of the nine Times Square the five. Now, let's look at our second radical. So we have the square of the 20 A squared. Well, the square. The 20 can be rewritten as the square of the four times five because the square root are sorry for is a perfect square. So we're right. That's a square. The four times square, the five and a square. Those are the perfect square. So I'm gonna leave that in its own radical Now for our last term, we can't simplify the square with a two way, so we're going to leave that as it's all right. So let's go back to the beginning. We're gonna bring down a discover the nine is three. So I'm actually good. Put that in front of the A and you can't simplify to square the five so We'll just bring that down, bring down the plus sign. Then we have the square of the four, which is to, and the square with a squared, which is a and again we can simplify to square the five. So we'll just bring that down. And as we mentioned earlier, we can't simplify this laster. All right, great. All of our radicals air simplified. But I know this. Our first two terms are like terms because both of their radical ends of the same so we can combine them. So it's add three. A Route five plus two, a Route five, which gives us five a Times Square, the five and we're just gonna bring down that last term because it doesn't have a like turn. And now we have simplified completely. So our final answer is five a Times Square, the five minus five times the square root of two a

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