How do you simplify the square root of -72 + square root of -50?

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Answer 1 · 2015-09-13T12:58:15

#sqrt(-72)+sqrt(-50) = 11i sqrt(2)#

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

If #a < 0# then #sqrt(a) = i sqrt(-a)#

So:

#sqrt(-72) = i sqrt(72) = i sqrt(6^2 * 2) = i sqrt(6^2) sqrt(2) = 6i sqrt(2)#

#sqrt(-50) = i sqrt(50) = i sqrt(5^2 * 2) = 1 sqrt(5^2) sqrt(2) = 5i sqrt(2)#

So:

#sqrt(-72)+sqrt(-50) = 6i sqrt(2) + 5i sqrt(2) = 11i sqrt(2)#

Note that the identity #sqrt(ab) = sqrt(a)sqrt(b)# does not hold if #a, b < 0#.

For example:

#1 = sqrt(1) = sqrt(-1 * -1) != sqrt(-1)*sqrt(-1) = -1#