What is the square root of -26 times the square root of -13?

1 Answer
George C.
Oct 8, 2015

sqrt(-26)*sqrt(-13) = -13sqrt(2)

Explanation:

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

If a < 0, then sqrt(a) = i sqrt(-a), where i is the imaginary unit.

So:

sqrt(-26) * sqrt(-13) = i sqrt(26) * i sqrt(13)

= i^2 * sqrt(26)sqrt(13)

= -1 * sqrt(26*13)

= - sqrt(13^2 * 2)

= - sqrt(13^2)sqrt(2)

= -13sqrt(2)

Note that you have to be careful with square roots of negative numbers. For example:

1 = sqrt(1) = sqrt(-1 * -1) != sqrt(-1)*sqrt(-1) = i^2 = -1

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