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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

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Q: Square root in denominator

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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).

That is called "rationalizing the denominator". It consists of multiplying the numerator and the denominator by specific terms, which include square roots. Examples:* If the denominator is root(2) (that is, the square root of 2), multiply numerator and denominator by root(2). * If the denominator is root(2) + root(3), multiply numerator and denominator by root(2) - root(3).

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.

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).

Depends on the situation. You usually have to multiply numerator and denominator by some number or expression. Examples: 1 / square root of 2 Here, you have to multiply numerator and denominator by the square root of 2. 1 / (square root of 2 + square root of 3) Here, you have to multiply numerator and denominator by (square root of 2 - square root of 3).

find the square root of the numerator and the square root of the denominator

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).

its false apex :)

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.

Only if the square root of the numerator and the square root of the denominator are both rational numbers.

The rules for "standard radical form" are that (a) there should be no perfect square within the radical sign; for example, square root of 12 is equal to square root of 4 x square root of 3 = 2 x square root of 3, and should be written as the latter; and (b) there should be no radical sign in the denominator. For example, if you have 1 / square root of 2, you multiply top and bottom by the square root of 2, to get a square root in the numerator, but none in the denominator.

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.

The fraction must be rationalized. Since it is the square root of x in the denominator, you are going to multiply the numerator and denominator by the square root of x. For simplicity of the problem, root will take the place of the symbol for square root: root(3y)/root(x) root(3y)*root(x)/root(x)*root(x) root(3xy)/x The simplified answer is going to be the square root of 3xy divided by x. Hope that helped.

In a way. You can multiply top and bottom by the square root of 2. This will not exactly make the expression simpler, but you'll get rid of the square root in the denominator (and transfer it to the numerator); this is considered to be the standard form for expressions which involve square roots. In other words, there should be no square roots in the denominator.

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

a+ square root of b has a conjugate a- square root of b and this is used rationalize the denominator when it contains a square root. If we want to multiply 5 x square root of 10 by something to get rid of the radical you can multiply it by square root of 10. But if we look at 5x( square root of 10 as ) 0+ 5x square root of 10 then the conjugate would be -5x square root of 10

Since the root is in the denominator of the exponent, just divide the 5 by the square root value (2), so the solution is x5/2.

The square root needs to be removed from the bottom. To do this multiply the numberater and denominator by the square root of 5. 125xsquare root of five over 5 25square root of 5 is the simplest answer.

It isn't clear what, exactly, you want to achieve. To write a fraction in standard form, it is customary to leave no radical in the denominator; in this case, for example, if you have square root of 2 in the denominator, you would multiply top and bottom by square root of 2, precisely to get rid of the radical in the denominator.

1/ square root of 50 = 1/(5*√2), which when rationalizing the denominator becomes (√2) / 10, and as a decimal is .1414213562...

A square root of a fraction applies to both the numerator and denominator, so it would be 6/8 or 3/4.

Yes. The square root of a fraction is the square root of the numerator over the square root of the denominator. First simplify the fraction (making mixed numbers into improper fractions). Now consider the numerator and denominator separately as whole numbers. Only perfect squares (the squares of whole numbers) have rational square roots. If either, or both, of the numerator and denominator is not a perfect square, the square root of the fraction will be irrational √(11/6) = (√11)/(√6). Neither 11 nor 6 is a perfect square, thus √(11/6) is irrational.

The details depend on the specific radical expression. Normally, you'll want to: * Avoid a perfect square under a radical sign. Take it out, by separating the radical into two parts. Example: root (x squared y) = root (x squared) x root (y) = x root (y). * Avoid a radical sign in the denominator. If you multiply numerator and denominator by the same square root, you get an expression in which there are roots in the numerator, but not in the denominator.

A square root is simplified when: -The radicand has no perfect square factors other than 1 -The radicand has no fractions -There are no square roots in the denominator *Radicand: the number and/or variables underneath the square root sign