# Examine, whether the following numbers are rational or irrational: (i)√ 7

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Examine, whether the following numbers are rational or irrational:

(i) 7

(ii) 4

(iii) 2+ 3

(iv) 3 +

(v) 3+ 5

(vi) ( 2- 2 )2

(vii) (2- 2)( 2+ 2)

(viii) ( 2 +3) 2

(ix) 5- 2

(x) 23

(xi) 225

(xii) 0.3796

(xiii) 7.478478……

(xiv) 1.101001000100001……

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7 is not a perfect square root, so it is an irrational number.

We have,

4 can be expressed in the form of , p/ q, so it is a rational number.

The decimal representation of 4 is 2.0.

2 is a rational number, whereas 3 is an irrational number.

Because, sum of a rational number and an irrational number is an irrational number, so 2 +3  is an irrational number.

2 is an irrational number. Also 3 is an irrational number.

The sum of two irrational numbers is irrational.

3+ 2 is an irrational number.

5 is an irrational number. Also 3 is an irrational number.

The sum of two irrational numbers is irrational.

3 +5 is an irrational number.

We have,

Now, 6 is a rational number, whereas 42 is an irrational number.

The difference of a rational number and an irrational number is an irrational number.

So, 6- 42  is an irrational number.

(2 - 2 ) is an irrational number.

We have,

Since 2 is a rational number.

(2 -2 )(2 +2) is a rational number.

We have,

The sum of a rational number and an irrational number is an irrational number, so 5+26  is an irrational number.

(2 +3)2 is an irrational number.

The difference of a rational number and an irrational number is an irrational number.

5- 2 is an irrational number.

23 = 4.79583152331........

225= 15 = 15/1

Rational number as it can be represented in p/q form.

0.3796

As decimal expansion of this number is terminating, so it is a rational number.

7.478478............ =7.bar 478

As decimal expansion of this number is non-terminating recurring so it is a rational number.