In Exercises 75–82, add or subtract terms whenever possible. 4⁵√2...

Question

In Exercises 75–82, add or subtract terms whenever possible. 4⁵√2+3⁵√2

Accepted Answer

Hello. Today we're going to add rational values together. So the rational values given to us is five times the square root of X plus 12 times the square root of four X plus eight times the square root of X over four. Now we want to go ahead and simplify any terms that need to be simplified. So looking at the first term which is five times the squared of X. That's already in its simplest form. So we're going to leave that alone for now. Now if we look at 12 times the square root of four X, this could be broken up as 12 times the square root of four times the square root of X. Now we can simplify the square root of X because we don't know what X is. But the square root of four can be simplified to two. So this leaves us with 12 times two times the square root of X. Which is then going to give us 24 times the square root of X. Now, if we look at the last term which is eight times the square root of X over four, we can go ahead and rewrite this as eight times the square root of X over the square root of four. Now we don't know what the square root of X is. So we're gonna leave that alone for now. But just like before we know that the square root of four could be rewritten as two. So we're gonna have eight times the square root of X. Over to multiplying this together is going to give me eight times the square root of X. All over two and eight and two could be simplified, two will become one and eight will become four. So we're left with four times the square root of X. Now, what we're gonna do is just go ahead and combine everything together into one statement. So that's gonna leave us with five times the square root of X Plus 24 times the square root of X Plus four times the square root of X. And now if you notice all these values have the square root of X in them, so we're gonna go ahead and add everything together. So five plus 24 plus four is gonna give us 33 times the square root of X. And that's gonna be our simplest solution which means that the solution to this problem is going to be be so I hope this helps you learn how to add rational values together. And I'll go ahead and see you all in the next video

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