Question

please do the requested questions in notebook ​

Answer 1

TO PROVE:-

3+2√5 IS AN IRRITATIONAL NUMBER.

SOLUTION:-

TO PROVE THAT ANY GIVEN STATEMENT IS IRRITATIONAL WE ALWAYS ASSUME THE OPPOSITE THAT IS TO TAKE IT RATIONAL.

HERE

3+2√5 IS RATIONAL (ASSUMING)

HENCE, 3+2√5 CAN BE WRITTEN IN THE FORM OF a/b....but the condition that

here a and b are co-prime.

Step by step explanation:-

3+2√5=a/b

after substituting

2√5=a/b-3

2√5=(a-3b)/b

Now substituting 2 from 2√5 to anothr side:-

√5=[(a-3b)/b] / 2

√5=1/2 * (a-3b)/b

√5=a-3b/2b

Here a-3b/2b is a rational number whereas √5 is an irritational number.

Since,rational is not equal to irritational

3+2√5 is not rational i.e. it is irritational.

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