simplify the expression...

Question

For problems 1–5, simplify the expression. Answers written in decimal form will not be accepted. (NO DECIMAL ANSWERS)

 
  1. square root of 96

  2. 8 times the square root of 63 x to the fifth power
  3. square root of 128 x to the fifth power y squared

  4. cube root of 32

  5. cube root of 56 x to the fourteenth power
 

Answer 1

2) 8√63x⁵=8√(9*7*x⁴*x)=8*3*x²√(7x)=24x²√7x

 

3) √128x⁵y²=√(64*2*x⁴*x*y²)=8*x²*y√2x=8x²y√2x

 

4) cube root(32)=cube root(8*4)=2cube root(4)=(2)³√4

 

5) cube root(56x¹⁴)=cube root(8*7*x¹²*x²)=2*x⁴*cube root(7x²)=2x⁴cube root(7x²)

Answer 2

May, 

 

Let me show you what they want for the first one and try the others, if not we can talk about them as well.

 

1. sqrt(96)

 

What we need to do is factor 96:

 

sqrt(96) = sqrt(4 * 4 * 6)

 

Now we have 4 * 4 in square root which we can pull outside of the root:

 

4 *sqrt(6)

 

With any of these problems you want to factor so you can pull out pairs of numbers. 

 

Does this help?