What is the square root of a negative number

It depends, but this is how I would do it:

Let's take the square root of -8 -->

First, I would take out an "i" and put it outside of the square root:

The i represents the negative sign. Then, I would treat the square root of 8 as a normal problem and simplify by factoring it:

Factors of 8: 2,2,2

Because you're looking for a square root and you can "loop" two 2s together, you can take one set out:

would be your final answer.

Hope I helped :)

answer: semi-infinite solid initially at a uniform temperature of 400 ◦c is cooled at its surface by convection. the cooling fluid at a constant temperature of 200 ◦c has a convective coefficient (ha) of 250 w/m2.k. the physical properties of the solid: k = 20 w/m.k and α = 4 * 10-5  m2/s. using δx = 0.04 m and δt = 10 s. write the finite difference equations describing the transient heat transfer of the first five δx and the temperature profile after 30 s.