Radical Trouble?

Question

Hello,
I am stuck on these two particular problems in dealing with radicals. I'm doing very well in algebra in general, but i'm getting stuck when it comes to roots and radicals. Could someone please check my work for me? I tried the best i could to figure them out. I would really appreciate it.

1.) Simplify-- √200x^3 = 10x^2√4x
2.) Find the product of (√3 -√2)(√3+√2) = √9 - √4

Answer 1

For the first one -- you started with 200x^3 under the radical sign. When you simplify 10x will come out and 2x will stay in, so your final answer will be 10x√(2x).

On the second one, you are correct, you just need to simplify your answer. Since √(9) = 3 and √(4) = 2, you have 3 - 2 = 1, so 1 is your final answer.

Answer 2

The first one you are struggling on. You were right to split the 200 into 100 and 2 and the x cubed into x squared times x. √200x^3=√100*2*x^2*x But since both the 100 and the x squared are perfect squares, you can square root them and put them in the front. √100=10 √x^2=x So you have 10x before the radical. Then, what's left in the radical is 2x.
So your answer should be 10x√2x

The second one, you just need to simplify a little further. What is the square root of 9? (3) What is the square root of 4? (2) What is 3-2? 1

Answer 3

Question 1:

(WHOOPS! I misread what you were saying, ignore what I said here, and use jkr17's answer.)

Question 2:

You started fine with the sqrt(9) - sqrt(4) step. Now simplify both of those radicals:

sqrt(9) - sqrt(4)
3 - 2
1

In general, it's the same concept of (x+y)(x-y) = x^2 - y^2, when you have similar binomial radicals with opposite signs between, just drop the radicals (but don't forget to square any rational coefficient) and make it a subtraction problem. This will be very handy when you're asked to rationalize denominators (which seems to be pretty soon).

Answer 4

In the first one, is the x^3 under the radical with the 200 or not?

Number 2 is correct though you may just want to re-write it as 3 - 2 = 1

Answer 5

The first one is incorrect, it should read
SQRT(200x^3)=10x*SQRT(2x) due to factoring

200=2*100
x^3=x*x^2

200*x^3=100x^2*2x

The SQRT(100x^2) = 10x, and the remaining terms stay under the bracket as SQRT(2x).

The last one you got correctly.

Hope this was clear enough.

Answer 6

1. 200 = 100*2 and x^3 = x*x^2
so SQRT(200x^3) = SQRT(100*2*x*x^2) = SQRT(100)*SQRT(2*x)(SQRT(x^2) = 10*SQRT(2*x^3)*x= 10x*SQRT(2x)

2.[SQRT(3) - SQRT(2)]*[SQRT(3) + SQRT(2)]
Multiply through to get:
SQRT(3)*SQRT(3) + SQRT(3)*SQRT(2) - SQRT(2)*SQRT(3) - SQRT(2)*SQRT(2)
Since SQRT(3)*SQRT(2) - SQRT(2)*SQRT(3) = 0
This becomes SQRT(3)*SQRT(3) - SQRT(2)*SQRT(2) = 3-2 = 1