Expert: Jack Cheng - 11/28/2006

Question
Can you assist with the following?

Simplify by factoring. Assume that all expressions under radicals represent nonnegative numbers.

The slashed represent the radical sign or check mark if you will.



1. /245k^7q8


Add or subtract. Then simplify by collecting like radical terms, if possible.
2. 21/ 5 - 13/ 5


Rationalize the denominator.  Assume that all expressions under readicals represent positive numbers.
3. -/ 25
    12

Solve.

4.  /4x-7-10 = 0

Find the length of the missing sice of the right triangle.  Round to three decimal places, if necessary.

5.  a= 12, c=20

Thanks

Answer
Hi Nicki,

Here's a hint for next time: square roots can be represented as (x)^(1/2). So the square root of 9 is (9)^(1/2). It's easier to read this way. (You can replace the 2 with n if you are finding the nth root).

1. I don't understand what I am supposed to do on this. You have two variables k and q, and where does the radical end?

2. I am assuming you mean 21(5)^(1/2) - 13(5)^(1/2). Let's treat (5)^(1/2) as x. What do you get for 21x-13x? Now substitute radical 5 back in for x and you have the answer.

3. I am assuming you mean -(25/12)^(1/2).
-(25/12)^(1/2) = -(25)^(1/2) / (12)^(1/2)
              = - (5 / (12)^(1/2)) * (12^(1/2) / 12^(1/2))
              = - 5 * 12^(1/2) / 12    (radicals cancel out)
              
4. The opposite of square root is square.  If you square both sides, what do you get?  (Opposites cancel out.)  Can you go on from there?

5. For this, you'll have to use the Pythagorean Thereom.
  a^2 + b^2 = c^2
  
You have a and c, now solve for b.  Remember, the square and square roots are opposites and cancel out.  However, (a^2 + b^2)^(1/2) does not equal a+b.

I hope this helps,
Jack