In Exercises 47 - 49, add or subtract terms whenever possible. 4√...

Question

In Exercises 47 - 49, add or subtract terms whenever possible. 4√72 - 2√48

Accepted Answer

Hello today we're gonna be working on subtracting rational values from each other. So the current rational values given to us is eight times the square root of 108 -2 times the square root of one, What we need to do is go ahead and simplify the square roots. And in order to do that, let's go ahead and rewrite the inside numbers as a product of prime numbers. So 100 8 could be broken up into two times 2 is a prime number, so I'm gonna go ahead and circle that and 54 can be broken up into nine times six. And both of these numbers could be broken up in even further as nine is three times three which are prime numbers and six is times two which are also prime numbers. So the first rational function is going to be eight times the square root of three times itself which is three cubed times two times itself twice which is two squared. Now I'm gonna go ahead and simplify 100 and 47 into a product of prime numbers. So 100 and 47 could be broken up into three times 49 three is a prime number. So I'm gonna go ahead and circle that. And 49 could be broken up into seven times seven which are prime numbers themselves. And that's going to leave us with two times the square root of seven times itself, seven squared times three. Since there's only one instance of three in this case, putting everything together is going to give us eight times the square root of three cubed times two squared minus two times the square root of seven squared times three. So looking at the first value, We have the square root of three cubed and the square root of two square, The square root of two squared is just going to give us two and the square root of three cued is the same thing as saying the square root of three times three times three. And this allows us to pull out one group of three, Which means that we are left with three times the square root of three. So putting that all together is going to give us eight times two times three times the square root of three. And we're gonna go ahead and subtract that from this other side. And on the other side we have the square root of seven squared and the square root of three. So the square root of three cannot be simplified any further. It's in it's simplest form, but the square root of seven squared is going to leave us with seven. That means that on the other side of this equation, we're going to have two times seven times the square root of three, multiplying the numbers together, is going to give us 48 times the square root of three minus 14 times the square root of three. And if you notice this number has the square root of three and this number has the square root of three. So now we can go ahead and subtract the numbers from each other. Doing so is going to give us 34 times the square root of three. That means that our solution is going to be C for this problem. So I hope this helps you figure out how to subtract square square roots and I'll go ahead and see you all in the next video.

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