Simplify each of the following expressions:

$left parenthesis space square root of 5 minus square root of 2 right parenthesis space left parenthesis square root of 5 plus square root of 2 right parenthesis$

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Solution

left parenthesis space square root of 5 minus square root of 2 right parenthesis space left parenthesis square root of 5 plus square root of 2 right parenthesis space equals left parenthesis square root of 5 right parenthesis squared minus left parenthesis square root of 2 right parenthesis squared

because

left parenthesis straight a minus square root of straight b right parenthesis end root left parenthesis straight a plus square root of straight b right parenthesis end root equals straight a squared minus straight b equals space 5 minus 2 space equals space 3

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