**√**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 4**√**2 is an irrational number.

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

So, 6- 4**√**2 is an irrational number.

(**√**2 - 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+2**√**6 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.