Question

Classify the following as rational (or) irrational

(i) √125

√5

(ii) √16 - √9 (iii) (√13 + 5)-5

(iv) √81 x √4 (v) 10-√7 (vi) √23 ÷ 7 V8​

Answer 1

Answer:

Hi heloooooo how to get it helps to make you feel

Answer 2

Answer:

(i)

2

1

Let us assume

2

1

is rational.

So we can write this number as

2

1

=

b

a

Here,aandbare two co-prime numbers and bis 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

a

b

=

2

b= a

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.

(ii)

7

5

Let us assume

7

5

is rational.

So, we can write this number as

7

5

=

b

a

Here,aandbare two co-prime numbers and bis not equal to zero.

Simplify the equation (1) divide by 7 both sides, we get

5

=

7b

a

Here, a and b are integers, so

7b

a

is a rational

number, so

5

should be a rational number.

But

5

is a irrational number, so it is contradictory.

Therefore, 7

5

is irrational number.

(iii)

6+

2

Let us assume

6+

2

is rational.

So we can write this number as

6+

2

=

b

a

Here,aandbare two co-prime number and bis not equal to zero.

Simplify the equation (1) subtract 6 on both sides, we get

2

=

b

a

− 6

2

=

b

a−6b

Here,aandbare integers so,

b

a−6b

is a rational

number, so

2

should be a rational number.

But

2

is a irrational number, so it is contradictory.

Therefore,

6+

2

is irrational number.

Step-by-step explanation:

Hi.

Hope it helps you..