How would I completely simplify these?


a) √10 x √8 I know that it is like 80x or maybe even 40x..


b) √24x^4 (24 x to the 4th power) / √3x I think it might be like 2x√2x?


c) √20 + 6√5 I'm guessing it might be 6√5 or 12√5?

When multiplying square roots of real numbers like these you simply multiply all the things that are under a square root sign and put the result under a square root, and then multiply those things that are not under a square root as normal. In other words:


a \sqrt b \ \times \ c \sqrt d = ab \sqrt {cd}


I'll help you with an example that is similar to problem (c): consider


3 \sqrt {32} \times 5 \sqrt 2 = 3 \time 5 sqrt {32 \times 2} = 15 \sqrt {64} = 15 \times 8 = 120.


Hope this helps.

For b, if this is the problem:


\frac {\sqrt {24 x^4}} {\sqrt {3x}}


then you can proceed like this:


\frac {\sqrt {24 x^4}} {\sqrt {3x}} = \sqrt {\frac {24} 3 \frac {x^4} x } = \sqrt {8 x^3} = \sqrt {4x^2 \times 2 x} = 2x \sqrt {2x}