Question

How do you simplify #5sqrt(-25) • i#?

Answer 1

#-25#

Explanation:

#5sqrt(-25)*i = 5isqrt(25)*i = 5i*5i = 25*i^2 = -25#

In common with all non-zero numbers, #-25# has two square roots.

The square root represented by the symbols #sqrt(-25)# is the principal square root #i sqrt(25) = 5i#. The other square root is #-sqrt(-25) = -i sqrt(25) = -5i#.

When #a, b >= 0# then #sqrt(ab) = sqrt(a)sqrt(b)#, but that fails if both #a < 0# and #b < 0# as in this example:

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