(2√24) / √54
= (2√4√6) / (√9√6)
= (4√6)/(3√6)
= 4/3
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The idea is to get rid of the square root in the denominator. For this purpose, you must multiply numerator and denominator by the square root of 6 in this case.
An example may help. If you have the fraction 1 / (2 + root(3)), where root() is the square root function, you multiply top and bottom by (2 - root(3)). If you multiply everything out, you will have no square root in the denominator, instead, you will have a square root in the numerator. If the denominator is only a root, eg root(3), you multiply top and bottom by root(3).
6
No, you can also use conjugates with more than one radical term. For example, if the denominator is root(2) + root(3), you can use the conjugate root(2) - root(3) to rationalize the denominator.
It looks like your question is [1-sqrt(3)] / [1+sqrt(3)], and you want to rationalize the denominator. If this is the case, multiply both numerator and denominator by (1-sqrt(3)), and get for the denominator = -2, and the numerator = 4 - 2*sqrt(3), so the answer is sqrt(3) - 2
Multiply everything by the square root of 3 minus the square root of 2 and then times that by 100 - 72 and divide that by 5
The idea is to get rid of the square root in the denominator. For this purpose, you must multiply numerator and denominator by the square root of 6 in this case.
Yes. For example, the conjugate of (square root of 2 + square root of 3) is (square root of 2 - square root of 3).
-26
An example may help. If you have the fraction 1 / (2 + root(3)), where root() is the square root function, you multiply top and bottom by (2 - root(3)). If you multiply everything out, you will have no square root in the denominator, instead, you will have a square root in the numerator. If the denominator is only a root, eg root(3), you multiply top and bottom by root(3).
6
No, you can also use conjugates with more than one radical term. For example, if the denominator is root(2) + root(3), you can use the conjugate root(2) - root(3) to rationalize the denominator.
If you want to rationalize the denominator, then multiply numerator & denominator by sqrt(5), so 8*sqrt(5)/5 = approx 3.578
It looks like your question is [1-sqrt(3)] / [1+sqrt(3)], and you want to rationalize the denominator. If this is the case, multiply both numerator and denominator by (1-sqrt(3)), and get for the denominator = -2, and the numerator = 4 - 2*sqrt(3), so the answer is sqrt(3) - 2
You cannot. The square root of 5 is irrational.
3.5714
You multiply the numerator and the denominator by the "conjugate" of the denominator. For example, if the denominator is root(2) + root(3), you multiply top and bottom by root(2) - root(3). This will eliminate the roots in the denonimator.