How do you simplify 5sqrt(-25) • i5√−25∙i?

1 Answer
George C.
Nov 14, 2015

-25−25

Explanation:

5sqrt(-25)*i = 5isqrt(25)*i = 5i*5i = 25*i^2 = -255√−25⋅i=5i√25⋅i=5i⋅5i=25⋅i2=−25

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

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

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

1 = sqrt(1) = sqrt(-1 * -1) != sqrt(-1)*sqrt(-1) = -11=√1=√−1⋅−1≠√−1⋅√−1=−1

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