## exercise 1.2 Class 10 Maths

### 1. Prove that âˆš5 is irrational.

Sol. Let us assume to the contrary that âˆš5 is an irrational number. So it can be written in the form of p/q where p and q are coprime integers and q is not equal to zero.

âˆš5= p/q

squaring both sides

(âˆš5)Â² = (p/q)Â²

5= pÂ²/qÂ²

pÂ²= 5qÂ² ,

so pÂ² is divisible by 5 hence p is also divisible by 5. So put p = 5m in above equation where m is some positive integer.

(5m)Â² = 5qÂ²

25mÂ² = 5qÂ²

qÂ²= 5mÂ² , so qÂ² is divisible by 5 hence q is also divisible by 5. It means p and q both are divisible by 5. Hence 5 is common factor of p and q. But it contradicts that p and q are coprime. Therefore our assumption is wrong. Hence âˆš5 is irrational.

### 2. Prove that 3 +2âˆš5 is irrational.

let us assume to the contrary that 3+ 2âˆš5 is a rational number. So

3 + 2âˆš5 = p/q , where p and q are coprime integers and q is not equal to zero

2âˆš5 = p/q -3

2âˆš5 = (p-3q)/q

âˆš5= (p-3q)/2q

since âˆš5 is irrational but (p-3q)/2q is rational.

And rational number can not equal to irrational number. So there is a contradiction. Our assumption is wrong, hence 3+2âˆš5 is irrational.

### 3. Prove that the following are irrational.

(i) 1/âˆš2 (ii) 7âˆš5 (iii) 6 + âˆš2

Ncert Solutions Class 10 Maths Exercise 1.1 https://10thmathsguide.com/exercise-11-class-10-maths/

Ncert Solutions Class 10 Maths Exercise 1.2

Ncert Solutions Class 10 Maths Exercise 2.1 https://10thmathsguide.com/exercise-21-class-10-maths/

Ncert Solutions Class 10 Maths Exercise 2.2

Ncert Solutions Class 10 Maths Exercise 3.1 https://10thmathsguide.com/exercise-31-class-10-maths/

Ncert Solutions Class 10 Maths Exercise 3.2 https://10thmathsguide.com/exercise-32-class-10-maths/

Ncert Solutions Class 10 Maths Exercise 3.3 https://10thmathsguide.com/exercise-33-class-10-maths/

Ncert Solutions Class 10 Maths Exercise 4.1 https://10thmathsguide.com/exercise-41-class-10-maths/

Ncert Solutions Class 10 Maths Exercise 4.2 https://10thmathsguide.com/exercise-42-class-10-maths/

Ncert Solutions Class 10 Maths Exercise 4.3 https://10thmathsguide.com/exercise-43-class-10-maths/

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exercise 1.2 Class 10 Maths exercise 1.2 Class 10 Maths

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