Question

proove that the following numbers are irrational 1/√2​

Answer 1

Answer:

10th

Maths

Real Numbers

Revisiting Irrational Numbers

Prove that the following ar...

MATHS

Prove that the following are irrational:

(i)

2

1

(ii) 7

5

(iii) 6+

2

MEDIUM

VIDEO EXPLANATION

ANSWER

(i)

2

1

Let us assume

2

1

is rational.

So we can write this number as

2

1

=

b

a

---- (1)

Here, a and b are two co-prime numbers and b is not equal to zero.

Simplify the equation (1) multiply by

2

both sides, we get

1=

b

a

2

Now, divide by b, we get

b=a

2

or

a

b

=

2

Here, a and b are integers so,

a

b

is a rational number,

so

2

should be a rational number.

But

2

is a irrational number, so it is contradictory.

Therefore,

2

1

is irrational number.

Answer 2

Step-by-step explanation:

Let us assume 1/√2 as rational

1/√2 = a/b ( where a and b are co-prime)

by reciprocal,

√2= b/a

b/a is rational

but, √2 is an irrational

Therefore, 1/√2 is an irrational

Hence proved

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