Question

Can you please help me reduce or simplify these radicals step by step??
1.) sqrt of 12 + the sqrt of 100
2.) cube rt of 16 * the cube rt of 3
I am really struggling!

Answer 1

\[\sqrt{12}+\sqrt{100}\]Okay so we cannot add them because of they don't have the same root. So what are the factors to 12? The factors are 3*2*2. So \[\sqrt{12}=2\sqrt{3}\]. The factors to 100 are 2*2*5*5, so it becomes just 10. To pull numbers out there MUST be a set of 2 because it is the square root. With 100 there was one set of 2 and one set of 5, you multiply them together to make 10. So I have this now: \[2\sqrt{3} + 10\]

Answer 2

completely, u were right :)

Answer 3

For the second one I chose to reduce first and then multiply. So I have 16 which factors to 2*2*2*2, this time I NEED three of the same number. So now I have 2 cubic root of 2 times the cubic root of 3. Now multiply them to make 2 cubic root of 6. 6 cannot be factored down any farther so that is your answer.