0
I will use "root" as a symbol for square root. I assume you want to get rid of the square root in the denominator; this will usually bring some square root into the numerator.
If you have the square root by itself, or as a factor, multiply numerator and denominator by this square root. Example:
3 / root(2) = 3 x root(2) / root(2) x root(2) = 3 x root(2) / 2.
If the square root is added or subtracted with something else, multiply with a "complement", as in the following example:
1 / root(2) + 5
The "complement" is the same expression, but changing the plus sign to a minus sign. Multiply numerator and denominator aby root(2) - 5:
root(2) - 5 / (root(2) + 5)(root(2) - 5)
= (root(2) - 5) / (2 - 25)
= (root(2) - 5) / -23
= -(root(2) - 5) / 23
Still curious? Ask our experts.
Chat with our AI personalities
Ezra
Steve
LaoAdd your answer:
Earn +20 pts
What is the process of eliminating a radical in the denominator of a fraction?
It is called rationalizing the denominator, and it is done by multiplying numerator and denominator by appropriate numbers. Note that if you do that, you will usually end up with radicals in the numerator. Examples: 1 / (square root of 2): Multiply numerator and denominator by the square root of 2. 1 / (square root of 2 + square root of 3): Multiply numerator and denominator by (square root of 2 - square root of 3).
What is the conjugate of a denominator?
This is related to the technique used to eliminate square roots from the denominator. If, for example, the denominator is 4 + root(3), you multiply both numerator and denominator by 4 - root(3). In this case, "4 - root(3)" is said to be the "conjugate" of "4 + root(3)". When doing this, there will be no more square roots in the denominator - but of course, you'll instead have a square root in the numerator.
What is 3 over the square root of 5?
You can get a decimal approximation with a calculator, with Excel, etc. But if you want to keep it as a square root, the "standard form" is considered to be one that has no square roots in the denominator. In this case, to get rid of the square root in the denominator, you multiply both numerator and denominator by the square root of 5, with the following result: 3 / root(5) = 3 root(5) / root(5) x root(5) = 3 root(5) / 5 That is, three times the square root of 5, divided by 5.
What does the denominator of a fractional exponent represent?
It represents the order of the root that needs to be calculated. A denominator of 2 means a square root. A denominator of 3 means a cube root. And so on.
Can 2 divided by 2 square root 3 be simplified?
Yes, the expression 2 divided by 2 square root 3 can be simplified. To simplify this expression, we need to rationalize the denominator. Multiplying both the numerator and the denominator by the conjugate of the denominator (2 square root 3), we get (2 * 2 square root 3) / (2 * 2 square root 3 * 2 square root 3). This simplifies to 4 square root 3 / 12, which further simplifies to square root 3 / 3.
