How do you simplify #sqrt(-5) + sqrt(-20)#?

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Answer 1 · 2015-10-16T23:41:13

#3sqrt(-5)" "#, or #" "3isqrt(5)#

The trick here is to try and rewrite #-20# as

#-20 = -5 * 4#

This means that #sqrt(-20)# can be written as

#sqrt(-20) = sqrt(-5 * 4) = sqrt(-5) * sqrt(4) = 2 * sqrt(-5)#

The expression becomes

#sqrt(-5) + 2sqrt(-5)#

These radical terms can be combined to give

#sqrt(-5) + 2sqrt(-5) = sqrt(-5) * (1 + 2) = 3sqrt(-5)#

If you're familiar with complex numbers, you can further simplify this expression by using

#i^2 = -1 implies sqrt(-1) = i#

This will get you

#3sqrt(-5) = 3sqrt(-1 * 5) = 3sqrt(-1) * sqrt(5) = 3 * i * sqrt(5)#