For questions on rationalising the denominator, the operation of rewriting a fraction in such a way that the denominator is free of square roots, cube roots, etc. The fraction can be a real number involving radicals, but also a function.
Questions tagged [rationalising-denominator]
87 questions
17
votes
4 answers
Rationalizing the denominator having square roots and cube roots
In middle-school mathematics, the teachers always tell you that if you have radicals on the denominator of a fraction, then it isn't fit to be a final answer - you have to rationalize the denominator, or get rid of all of the radicals in the…
Franklin Pezzuti Dyer
- 39,754
- 9
- 73
- 166
2
votes
4 answers
Rationalising the denominator surds
I have been struggling on this question. I don't understand how to change a negative surd fraction to a positive surd fraction.
Question: Rationalise and simply
$$\frac{2}{1+{\sqrt 6}}$$
What I did:
$\frac{2(1-{\sqrt 6})}{(1+{\sqrt…
2
votes
2 answers
common denominator
What is the common denominator of the following:
$x^2-x$ and $2x$, $x^2$
(the first is the one side, and the other 2 are another side of the formula)
The full formula is:
$1/(x^2-x) = 1/2x + 1/x^2$
P.G
That's not homework. I am a mother of 3 trying…
Dejel
- 139
1
vote
1 answer
How do I rationalize the following denominator
$$\frac{-2}{3\sqrt\frac{5}{12u}}$$
What I did:
turned denominator and numerator into square roots
$\frac{\sqrt5}{\sqrt{12u}}$
simplified denominator to
$2\sqrt{3u}$ and $2$ is multiplied by $-2/3$ to make $-4/3 \sqrt 5/\sqrt{12u}$
I then multiplied…
Ben
- 19
0
votes
2 answers
Rationalize the denominator in $\frac{1}{1+ \sqrt2+ \sqrt3}$
I found this method in a book.
To rationalize the denominator in $\frac{1}{1+\sqrt2 +\sqrt3}$,
we multiply denominator and numerator so that we get the denominator $$(1+\sqrt2 +\sqrt3)(1+\sqrt2 -\sqrt3)(1-\sqrt2 +\sqrt3)(1-\sqrt2 -\sqrt3)$$.
The…
Aditya
- 930
0
votes
1 answer
rationalize this expression (in the description)
I tried changing the surd in the denominator into a fractional indices but I have no idea what to do after that
mhm
- 129
- 6
0
votes
2 answers
Simplify by rationalizing the denominator.
I have the problem:
Write
$$\frac{4 \sqrt{2} + 6 \sqrt{3} + 10 \sqrt{5}}{(\sqrt{2} + \sqrt{3} + \sqrt{5})^2}$$in simplest form.
I have tried simplifying by doing this: $$\frac{4(\sqrt2+\sqrt3+\sqrt5)+2\sqrt3+6\sqrt5}{(\sqrt2+\sqrt3+\sqrt5)^2}$$
but…
Mike Smith
- 1,122
- 6
- 26
0
votes
1 answer
Rationalising term
What will be the rationalizing term for $30\sqrt 2 + 24 + 20 \sqrt 6$? It cannot be $30 \sqrt 2 - 20\sqrt 6$. Neither can it be $30 \sqrt 2+ 20 \sqrt 6 - 24$ because the product of these with the denominator will again contain a square root.
Please…
Ram Keswani
- 1,003
0
votes
1 answer
When is $\frac{a\sqrt{2}+b}{b\sqrt{2}+c}$ an integer?
$\frac{a\sqrt{2} + b}{b\sqrt{2}+c}$ is a number, where $a, b, c$ are integers. What should be the condition for above number to be an integer? One possible solution is $a = b = c$. Other solutions would be a great help.
Archis Welankar
- 15,910
-1
votes
2 answers
Rationalizing Denominators of Radical Expressions
The task is to get rid of square root in the denominator in the following equation: $\frac{2\sqrt{7} + \sqrt{14}} {\sqrt{7}} $. To do so I multiplied both denominator and nominator by $\sqrt{7}$ and my result is as follows:
$$\frac{2\sqrt{7} +…
Marcel
- 101