How do you simplify #sqrt(49-x^2)#?

1 Answer
George C.
Jan 31, 2016

This expression cannot be simplified, but it can be re-expressed:

#sqrt(49-x^2) = sqrt(7-x)sqrt(7+x)#

Explanation:

If #a >= 0# or #b >= 0# then #sqrt(ab) = sqrt(a)sqrt(b)#

For any Real number #x#, at least one of #7-x >= 0# or #7+x >= 0#, so we find:

#sqrt(49-x^2) = sqrt((7-x)(7+x)) = sqrt(7-x)sqrt(7+x)#

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