NCERT solution Class 10 real numbers

NCERT Solutions

Class 10 Maths

Real Numbers

NCERT Questions

Ex. 1.1 Q1
Ex. 1.1 Q2
Ex. 1.1 Q3
Ex. 1.1 Q4
Ex. 1.1 Q5
Ex. 1.1 Q6
Ex. 1.1 Q7
Ex. 1.2 Q1
Ex. 1.2 Q2
Ex. 1.2 Q3

Ex. 1.2 Q3

Prove that the following are irrationals:

(i) 1/√2

(ii) 7√5

(iii) 6 + √2

(i) Let take that 1/√2 is a rational number.

So we can write this number as

1/√2 = a/b

Here a and b are two co prime number and b is not equal to 0

Multiply by √2 both sides we get

1 = (a√2)/b

Now multiply by b

b = a√2

divide by a, we get

b/a = √2

Here, a and b are integer, so b/a is a rational number. It means √2 should be a rational

number. But √2 is an irrational number. Hence, it is contradict the fact.

Hence, 1/√2 is an irrational number

(ii) Let take that 7√5 is a rational number.

So, we can write this number as

7√5 = a/b

Here a and b are two co prime number and b is not equal to 0

Divide by 7 we get,

√5 =a/7b

Here, a and b are integer, so a/7b is a rational number.

It means √5 should be a rational number but √5 is an irrational number.

So, it is contradict the fact.

Hence, 7√5 is an irrational number.

(iii) Let take that 6 + √2 is a rational number.

So, we can write this number as

6 + √2 = a/b

Here a and b are two co prime number and b is not equal to 0

Subtract 6 both side, we get

√2 = a/b – 6

√2 = (a - 6b)/b

Here ,a and b are integer, so (a - 6b)/b is a rational number.

It means √2 should be a rational number but √2 is an irrational number.

So, it is contradict the fact.

Hence, 6 + √2 is an irrational number.

Video solution:

Real Numbers Class 10 Maths NCERT Chapter 1 NCERT Solutions

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NCERT solutions of Real Numbers Class 10 Maths - all questions of all exercises are solved. Q. No. 1, 2, 3, and so on. Complete explanation and detailed solution makes them the best videos for Class 10 Maths Real Numbers NCERT solutions.