## 2. Rationtinalise the denominator of 1/root 9 + 2root 2 ​

Question

2.
Rationtinalise the denominator of 1/root 9 + 2root 2 ​

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2 weeks 2021-09-09T23:26:51+00:00 2 Answers 0 views 0

1. Step-by-step explanation:

1. Multiply Both Top and Bottom by a Root

Sometimes we can just multiply both top and bottom by a root:

Example: 1 divide root 2 has an Irrational Denominator. Let’s fix it.

Multiply top and bottom by the square root of 2, because: √2 × √2 = 2:

rationalized

Now the denominator has a rational number (=2). Done!

Note: It is ok to have an irrational number in the top (numerator) of a fraction.

2. Multiply Both Top and Bottom by the Conjugate

There is another special way to move a square root from the bottom of a fraction to the top … we multiply both top and bottom by the conjugate of the denominator.

The conjugate is where we change the sign in the middle of two terms:

Example Expression Its Conjugate

x2 − 3 x2 + 3

Another Example Its Conjugate

a + b3 a − b3

It works because when we multiply something by its conjugate we get squares like this:

(a+b)(a−b) = a2 − b2

Here is how to do it:

Example: here is a fraction with an “irrational denominator”:

13−√2

How can we move the square root of 2 to the top?

We can multiply both top and bottom by 3+√2 (the conjugate of 3−√2), which won’t change the value of the fraction:

13−√2 × 3+√23+√2 = 3+√232−(√2)2 = 3+√27

(Did you see that we used (a+b)(a−b) = a2 − b2 in the denominator?)