Rationalize the denominator and simplify.

Question

What is the sum for 3 divided by the square root of 6?

Answer 1

The standard form for radicals does not allow a radical to remain in a denominator.

Radicals in denominators are easy to remove by multiplying the fraction by a fancy form of the number 1.

Multiplying by 1 does not change its value but the fancy form changes its look.

So the fancy form of 1 in this problem is

√6

√6

So here we go

3 X √6 = (3 √6) = 3 √6 = √6

√6 √6 √6 √6 6 2

The value is the same as the original problem but the radical has been removed from the denominator.

Success.

(If you want to verify your answer, put the original problem into a calculator to make it a decimal, then put your answer into the calculator and see if you get the same decimal.).

Answer 2

NOTE that when you multiply and divide by the same number, the value of the number does not change because you are multiplying by 1.

As seen below, √6 / √6 (=1) is used. The radical in the denominator is converted from an irrational number to a rational number. You still have a radical in the numerator, but that is considered acceptable.

You have changed the look of your number, but you have not changed its value.

This technique produces a unique, standard version of this number. It can be compared to simplifying a fraction. 1/2 = 4/8, but only 1/2 is considered appropriate in math classes for a final answer.

Rationalizing denominators will be expected of you from now on in math classes, just as how reducing fractions has been for years.

Actually, your problem was an easier case. I expect your teacher will next show you how to remove the radical from problems like this:

4 / ( 3 - √5 )

Answer 3

3 / √6

(3 √6) / (√6 √6)

(3 √6) / 6

√6 / 2