Question

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

Answer 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?)

Answer 2

Answer:

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