SOLUTION: rationalize the denominator of the fraction.3 sqrt 3 over 3 sqrt 7 i came up with 3 sqrt 147 over 7 but i have no idea if this is correct.thanks in advance for your help .also rewr

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: rationalize the denominator of the fraction.3 sqrt 3 over 3 sqrt 7 i came up with 3 sqrt 147 over 7 but i have no idea if this is correct.thanks in advance for your help .also rewr      Log On


   

Question 139361: rationalize the denominator of the fraction.3 sqrt 3 over 3 sqrt 7 i came up with 3 sqrt 147 over 7 but i have no idea if this is correct.thanks in advance for your help .also rewrite 5 sqrt c with a small 2 at the top of the c.for this one i got c 2/5
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
%283sqrt%283%29%29%2F%283sqrt%287%29%29

Unless the number under the radical is a perfect square, like 4, 9, 16, 25..., then the square root is an irrational number. A rational number is one that can be expressed as the quotient of two integers, p%2Fq where p and q are integers. An irrational number cannot be expressed this way.

So rationalizing a denominator means 'get that nasty radical the heck out of my denominator'

In this problem, we need to multiply the denominator by sqrt%287%29, so the denominator will become 3%2Asqrt%287%29%2Asqrt%287%29=3%2A7=21. BUT, we have to do so in such a way that we don't change the value of the overall fraction. Since we know that anything multiplied by 1 is itself (a%2A1=a no matter what a is), we can multiply the fraction by 1 in the form of sqrt%287%29%2Fsqrt%287%29. (a%2Fa=1 no matter what a is).

But first a rule about radicals: No matter what a and b are (as long as they are positive) we can say that sqrt%28a%29%2Asqrt%28b%29=sqrt%28ab%29.

Now:

.

So we have a new fraction that is equivalent to the original, but has a rational number (21) in the denominator. Done.

For your other problem, I think you mean 5sqrt%28c%5E2%29. I'm a little concerned that you are referring to c%5E2, meaning 'c squared' as "c with a small 2 at the top of the c" and you are in a class where you are being asked to rationalize denominators. The square root of something squared is just that thing, so sqrt%28c%5E2%29=c, and your simplified expression is just 5c. But my concern is that your rather unsophisticated use of terminology indicates that you might have a significant gap in your grasp of algebraic fundamentals that can't be corrected by visiting help sites like this one. You should see your instructor and get him/her to provide you with some intensive remedial instruction.