Question

I have an algebra question that says i have to simplify the fraction by rationalizing the denominator of the fraction 4 sqrt 6/sqrt 30.
problem is, idk what rationalizing is. well, i looked it up, but can someone help me rationalize the denominator of this fraction, then simplify?

Answer 1

4√6/√30
first of all you have to know the difference between an irrational or rational number
a rational number is one which can be expressed as a fraction of the form a/b, where
a and b are integers, and b ≠ 0
an irrational number obviously cannot be expressed as a fraction in that form, usually they
are square roots, cube roots etc
4√6/√30 contains an irrational number at the bottom, we want it to be rational
4√6/√30 * (√30/√30) <---- I multiplied by 1, so not changing its value but merely its appearance
= 4√180/30
= 4√36√5 / 30
= 24√5 / 30.
= 4√5 / 5 <---- notice the denominator is no longer irrational.

If you have a monomial irrational at the bottom, simply multiply top and bottom by that irrational
based on the fact that √x * √x = x

Your next step would be rationalizing denominators that are binomials
e.g.
4/(√6 + 7) , google and look up examples of "rationalizing the denominator"