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

Question

Perform the indicated operations. Assume all variables represent positive real numbers. 8√(2x) - √(8x) + √(72x)

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 minus the square root of 75 times Y plus the square root of 300 times Y. Now, in order to simplify this expression, we're going to need to first simplify the three given square roots in the first term the square root of three Y is already in its simplest form. So we're going to leave it as is in the second square root we can rewrite 75 to be 25 times three. And in the third square root we can rewrite 300 to be times three. So if we make these substitution, what we are left with is seven times the square root of three y minus the square root of 25 times three times Y, which is going to be three Y plus the square root of 100 times three times Y, which is going to be three Y. Now, one thing to note here is that 25 and 100 are perfect squares. 25 can be rewritten as five squared and 100 can be rewritten as 10 squared. So what the square root allows us to do is to take out any numbers in pairs of two here, five squared can be rewritten as five times five, which acts as a pair of two. So we can go ahead and take how five from the square root. And the same thing can be applied 10 10 squared. We can go ahead and remove 10 squares outside of the square root and what that's going to leave us with is seven times the square root of three, y minus five times the square root of three, Y plus 10 times the square root of three. Y. Now notice that we have a square root of three Y in each term. So we can go ahead and combine all three of the square roots into a single square root of three Y by adding up the coefficients By adding up the coefficients we get 7 -5 plus 10 times the square root of three, Y. Seven minus five is going to give us two and two plus 10 is going to leave us with 12. So what we are left with is 12 times the square root of three Y. Which is going to be the simplified form of the given expression. And with that being said, the answer to this problem is going to be a 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. 8√(2x) - √(8x) + √(72x)

Key Concepts

Radical Expressions

Simplifying Radicals

Combining Like Terms

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