Perform the operation and/or simplify each of the following. Assu...

Question

Perform the operation and/or simplify each of the following. Assume all variables represent positive real numbers. (2 + √3) (2 - √3)

Accepted Answer

Hello today we're going to be evaluating the given expression. So what we are given is seven plus the square root of times the quantity seven minus the square root of 13. Now, in order to simplify the quantities together, we're going to need to foil the two quantities together. So in order to foil them, we're going to take the first term of the first quantity which is seven and multiply it to the first term of the second quantity which is going to be seven and that is going to give us seven times seven. Next we're going to take seven and multiply two. The second term of the second quantity which is negative 13 and seven times the negative square root of 13 is going to give us negative seven times the square root of 13. Next we're going to take the second term of our first group which is going to be the square root of 13 and multiply it to the first term of the second group which is positive seven and seven times the square root of 13 is going to give us positive seven square root of 13. And finally we're going to take the positive square root of 13 and multiply it to the negative square root of 13. Now a positive number times a negative number is going to give us a negative number and what we have is square root of 13 times square root of 13. So let's go ahead and simplify this seven times seven is going to give us 49 and negative seven square to 13 plus seven square to 13 is just going to cancel each other out. Then we're going to be subtracting the square root of 13 times the square root of 13. Now, one thing to note here is that since both of the square root of 13 are under the same value of square root, we can go ahead and combine this as a single square root. So the square root of 13 times the square root of 13 is going to be the square root of 13 times 13. And the square root of 13 times 13 can be simplified to be the square root of 13 squared. Now, what's going to happen here is that the square root is going to cancel out what the innermost exponent which is going to be too and what we are left with is going to be positive 13. So what we have now is 49 -13 and 49 -13 is going to leave us with 36, which 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 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

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Perform the operation and/or simplify each of the following. Assume all variables represent positive real numbers. (2 + √3) (2 - √3)