what is the square root of -2?\
how would you solve this equation:
square root of -2(square root of -18) + square root of -25?
http://www.purplemath.com/modules/complex.htm
sqrt(-2) * sqrt(-18) + sqrt(-25).
sqrt(2*-1) * sqrt(9*2*-1) + sqrt(25*-1)= i*sqrt(2) * 3i*sqrt(2) + 5i =
3i^2 * 2 + 5i =
3(-1) * 2 + 5i =
-6 + 5i.
The square root of -2 is not a real number, as the square root operation is only defined for non-negative real numbers. However, in complex numbers, the square root of -2 can be represented as √(-2) = i√2, where "i" is the imaginary unit (√(-1)).
To solve the equation √(-2) (√(-18)) + √(-25), we can break it down step by step:
1. Start by simplifying each square root separately:
√(-2) = i√2
√(-18) = i√18
2. Substitute the simplified square roots back into the original equation:
i√2 (i√18) + √(-25)
3. Simplify further within the parentheses:
(i√2)(i√18) can be rewritten using the property that i² = -1:
(i)(i)(√2)(√18) = -√2√18
4. Simplify the remaining square root:
√(-25) = i√25 = i5
5. Substitute all the simplified square roots back into the equation:
-√2√18 + i5
At this point, the equation is simplified as much as possible with the given information.