in-3-38-write-each-expression-in-simplest-form-variables-in-the-radicand-with-an-even-index-are-n-19

Question

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.
$$
a \sqrt{45}+\sqrt{20 a^{2}}-5 \sqrt{2 a}
$$

Julie Silva · Accepted Answer

we&#x27;re being asked to simplify the given expression. So the first thing we need to do is simplify each of our radicals. So let&#x27;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&#x27;m gonna rewrite this as a times the square of the nine Times Square the five. Now, let&#x27;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&#x27;re right. That&#x27;s a square. The four times square, the five and a square. Those are the perfect square. So I&#x27;m gonna leave that in its own radical Now for our last term, we can&#x27;t simplify the square with a two way, so we&#x27;re going to leave that as it&#x27;s all right. So let&#x27;s go back to the beginning. We&#x27;re gonna bring down a discover the nine is three. So I&#x27;m actually good. Put that in front of the A and you can&#x27;t simplify to square the five so We&#x27;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&#x27;ll just bring that down. And as we mentioned earlier, we can&#x27;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&#x27;s add three. A Route five plus two, a Route five, which gives us five a Times Square, the five and we&#x27;re just gonna bring down that last term because it doesn&#x27;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

Julie Silva · Answer

we&#x27;re being asked to simplify to given expression. Remember, when you subtract radicals, you need to simplify both radicals first. Well, let&#x27;s take a look at the square root of eight A. Well, the perfect square four goes into 82 times. So I&#x27;m going to rewrite this as the square of the four times the square root of two way because four times to a is a day now I can&#x27;t simplify the square of the two way, so I&#x27;m gonna lead. That is this. Now let&#x27;s go back to our first term. We have the square with a four witches too. And we can&#x27;t simplify the square of the two way. So we bring that down. So we have two minus the square that you weigh minus the square that you weigh. All right, so now both radicals air simplified and we can combine these because both radic cans of the same. So we just combine the coefficients which remembered the coefficient of our second term is one. Well, two minus one is just one. So we&#x27;re just left with the square root of two a

Finian Lickona · Answer

in this exercise, we&#x27;re going to simplify the expressions for a B squared minus a B squared. Okay, so it&#x27;s easy to recognize immediately. Four is a perfect square. B squared is a perfect square, so we can fact those both out of the radical as to be in there. We are left with a inside the radical. Ah, And then, of course, this b squared can also be factored out. So with this well, it wouldn&#x27;t be radical. A So now we simply have to be radical. A minus be radical. A. So that means our final answer is simply be radical.

Julie Silva · Answer

we&#x27;re being asked to simplify the given expression. So remember, whenever you add radicals, you want to simplify all your radicals first. So let&#x27;s start with our first radical. We have the square root of 250 a square. Well, 250 is not a perfect square, however, the perfect square 25 devise into it 10 times. So I&#x27;m going to rewrite it as two square with a 25 times to square the 10 and then I&#x27;ll leave my a square than his own radical. Okay, so now let&#x27;s take a look at the second radical. We have the square of the 10 A squared Well, we can simplify the square, the 10 fervor because no perfect square goes into 10 evenly. However, a squared is a perfect square to square. The H word is a so we can simplify this toe a times to square the 10. All right, let&#x27;s go back to the first radicals and simplify well, the square, the 25 5, the square root of a square, this A and the square. The 10 can&#x27;t be simplified, so I&#x27;ll just bring that down. Then we&#x27;ll bring down our second radical, a Britain. So now both radicals air simplified and these two radicals are Expressions are right terms because both radic cans of the same. So we just need to combine the coefficients well. Five a plus a is six a. So our final answer will be six a Times Square the 10.

Julie Silva · Answer

we&#x27;re being asked to simplify the given expression. So the first thing we need to do when subtracting radicals is make sure both radicals air simplified. So let&#x27;s start with our first radical. Well, we have the square of the 63 a square, The perfect squared nine goes into 63 seven times, so we can rewrite that as the square of the nine times to square the seven and the square. The A squared is just a so I&#x27;m gonna bring that a in front because it is a perfect square. All right, let&#x27;s take a look at our second radical. We have the square with a 45 a square again. The perfect square nine goes into 45 5 times, so we&#x27;ll rewrite that a square than nine times square. The five and then we have the square, the bass squared, which again? It&#x27;s a perfect square. It&#x27;s just a so I&#x27;ll put that in front. All right, so now let&#x27;s simplify our radicals. So from the first term we can bring down the A. Then we have the square of the nine is just three, so put that in front. But then we can&#x27;t simplify to square the seven solely that now, from our second term offering down the A, the square with the nine is three. And then we have to square the five, which can&#x27;t be simplified. Sobering that down. Okay, great. Now, both far radicals have been simplified. However, they&#x27;re not like terms because both radic cans are different. We have to square the seven and the square of the five, which means we can&#x27;t simplify any fervor. So our final answer is three a brute seven minus three, a brute five.

Julie Silva · Answer

for being asked to simplify the given expression. So we have the square with the two plus fiber to will remember, you can combine like radicals if they have the same radic. And in this case, because our Braddock an for both of our radicals are too we can combine these these air like radicals. So all we need to do is combine the coefficients. Remember, In the first radical to square, the two is coefficient is one So we&#x27;re gonna combine the coefficients. So we have one plus five, which is six. And then we bring down our radical the square the to. So our final answer is six route to

Problem

In $3-38$ write each expression in simplest form.…

Problem 21 Hard Difficulty

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.
$$
a \sqrt{45}+\sqrt{20 a^{2}}-5 \sqrt{2 a}
$$

Answer

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

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

Algebra 2 and Trigonometry

Ann Xavier GantertAlgebra 2 and Trigonometry

Ann Xavier Gantert

Algebra 2 and Trigonometry