Question

The rationalising factor of 1/(1+√2)

Answer 1

Answer:

1-root 2

Step-by-step explanation:

...hope it helps

Answer 2

Given:

An irrational number 1/(1+√2).

To Find:

The rationalizing factor of 1/(1+√2).

Solution:

The given problem can be solved using the concepts of rationalization.

1. The given fraction is 1/(1+√2).

2. Consider a fraction of form 1/(a+√b),

=> Rationalization refers to the conversion of the decimal into a rational value from the irrational value.

=> (a+√b) can be converted into a rational value by multiplying it with (a -√b),

=> (a+√b) x (a-√b) = a² - b, ( It is a rational value).

=> The rationalizing factor of the form (a+√b) is (a-√b).

3. Using the above point, the denominator of the fraction 1/(1+√2) can be rationalized as follows,

=> 1/(1+√2) =$\frac{1*(1-\sqrt{2}) }{(1+\sqrt{2}) * (1-\sqrt{2)} }$,

=> (1 - √2)/ ( 1 - 2),

=> - ( 1 - √2),

=> √2 -1.

Therefore, the rationalizing factor of the fraction 1/(1+√2) is 1/(1-√2)