Question Video: Evaluating Algebraic Expressions Involving Irrational Numbers Mathematics • 10th Grade

Given that ๐‘Ž = โˆš(5) + 8 and ๐‘ = โˆš(5) โˆ’ 8, find the value of ๐‘Ž + ๐‘.

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Video Transcript

Given that ๐‘Ž equals the square root of five plus eight and ๐‘ equals the square root of five minus eight, find the value of ๐‘Ž plus ๐‘.

We have ๐‘Ž plus ๐‘, where ๐‘Ž is the square root of five plus eight and ๐‘ is the square root of five minus eight. And weโ€™re adding these values together. We have plus eight minus eight, and eight minus eight is zero. At this point, you might not always remember how to handle the square root of five plus the square root of five. I think itโ€™s sometimes helpful to think of it in terms of variables.

Imagine we were adding ๐‘ฅ plus ๐‘ฅ. Can we simplify this any further? Well, yes. ๐‘ฅ plus ๐‘ฅ equals two ๐‘ฅ. And we can treat the square root of five in the same way. The square root of five plus the square root of five equals two times the square root of five. Given these values for ๐‘Ž and ๐‘, the value of ๐‘Ž plus ๐‘ would be two times the square root of five.

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