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?
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"
Of course! I'd be happy to help you understand how to rationalize the denominator of the fraction 4√6/√30.
Rationalizing the denominator means getting rid of any radicals (square roots) in the denominator of a fraction. To do this, we aim to eliminate the square root from the denominator while maintaining the value of the fraction. In this case, we have the square root of 30 in the denominator.
To rationalize the denominator, we need to multiply the numerator and the denominator by the conjugate of the denominator. The conjugate of a binomial is obtained by changing only the sign between the terms. In this case, the conjugate of √30 is -√30.
Now, let's perform the rationalization step by multiplying both the numerator and the denominator by -√30:
(4√6/√30) * (-√30/-√30)
This gives us (-4√6*-√30) / (√30*-√30)
Multiplying, we get (4√6 * √30) / (√30 * √30)
Simplifying further, we have (4√6√30) / (√30√30)
To simplify, notice that the square root of 30 can be written as the square root of 6 multiplied by the square root of 5 (since 30 = 6 * 5).
So, our expression becomes (4√6 * √6 * √5) / (√6 * √6 * √5)
The square root of 6 squared cancels out, so we are left with:
(4 * √5) / √5
Finally, simplifying we get:
(4/1) = 4
Therefore, the simplified form of the fraction 4√6/√30 after rationalizing the denominator is 4.