In Exercises 1–38, multiply as indicated. If possible, simplify a...

Question

In Exercises 1–38, multiply as indicated. If possible, simplify any radical expressions that appear in the product.(√6 + √2) (√6 - √2)

Accepted Answer

Hello, today we're gonna be simplifying the given expression. So what we are given is the quantity square root of 13 plus the square root of 17, multiplied by the quantity the square root of 13 minus the square root of 17. Now, what we're going to do is we're going to simplify this using the method of the difference of squares. The difference of square states that if you have the binomial A squared minus B squared, then this is going to factor to A plus B multiplied by A minus B. See in the current form of the expression, the expression currently matches the right hand side of the property for the difference of squares. Here, we're going to allow 13 to be a And we're going to allow 17 to be B. So if we wanted to use the difference of squares to simplify this, we're going to allow A to equal to the square root of 13. And we're going to allow B to equal to the square root of 17, then we're going to put it into the form of A squared minus B squared. And that is going to give us the square root of 13 squared minus the square root of 17 squared. Now, the exponent of two is going to allow us to cancel out the square roots. And that is going to leave us with 13 -17, which is going to simplify to negative four. And this is going to be the simplest form of the given expression. And with that being said, the answer to this problem is going to be B 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.

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In Exercises 1–38, multiply as indicated. If possible, simplify any radical expressions that appear in the product.(√6 + √2) (√6 - √2)

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