Perform the indicated operations. Assume all variables represent ...

Question

Perform the indicated operations. Assume all variables represent positive real numbers. 3√72m² - 5√32m² - 3√18m²

Accepted Answer

Hello. Today we're going to be rewriting the given expression in its simplest form. So what we are given is seven times the square root of three, Y squared minus the square root of 75 Y squared plus the square root of 300 y squared. Now the square root allows you to take out any number that are in multiples of two times itself. And what we have in each term is y squared, Y squared can be rewritten as y times itself two times. So since why is being multiplied by itself two times the square root is going to allow us to take out the y squared as a single. Why? So doing that to each term is going to allow us to rewrite the expression as seven times Y times the square root of three minus y times the square root of 75 plus Y times the square root of 300 so now what we need to do is go ahead and simplify the square roots. The square root of three cannot be simplified any further. So we're going to leave the first term as is 75 can be rewritten as 25 times three And 300 can be rewritten as 100 times three. So if we rewrite the inside terms, what we can rewrite the expression two is seven, Y times the square root of three minus Y. Times the square root of 25 times three plus Y times the square root of 100 times three. Now, one thing to note here is that 25 and are perfect squares. 25 can be rewritten as five times itself two times which itself can be rewritten as five squared and 100 can be rewritten as 10 times itself two times which itself can be rewritten as 10 squared. So what we have is five squared times three and squared times three in the 2nd and 3rd term. And again the square root allows us to remove any numbers that are in pairs of two. So we can remove five squared as a single five and we can remove squared as a single 10. And doing this can allow us to rewrite the expression as seven y times the square root of three minus five times Y which is going to give me five y times the square root of three plus 10 times Y. Which is going to give me 10 y times the square root of three. So notice that every term has the square root of three in it. So we can go ahead and combine all three terms into a single square root of three by combining the coefficients together and combining the coefficients together is going to give us seven y minus five, Y plus 10 y times the square root of three, seven y minus five Y is going to give us two Y and two, Y plus 10. Y is going to give us 12 Y. So what we are left with is 12 y times the square root of three. And this is going to be the simplified version of the given expression. And with that being said, the answer to this problem is going to be be so. I hope this video helps you in understanding how to approach this problem, and I'll go ahead and see you all in the next video.

Perform the indicated operations. Assume all variables represent positive real numbers. 3√72m² - 5√32m² - 3√18m²

Key Concepts

Radical Expressions

Simplifying Radicals

Combining Like Terms

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