Question

1,) Which of the following is an irrational number?

Answer 1

Im not 100% sure but
1.square root of 0.4

2. -7.888888888888

Answer 2

Answer:

Ques 1)

 B)   $\sqrt{0.4}$

Ques 2)

D)   $\sqrt{0.025}$

Step-by-step explanation:

We know that an irrational number is a number which could not be expressed in the form of p/q where p belongs to integers and q belongs to natural numbers.

Also the decimal expansion of an irrational number is:Non-terminating and non-repeating.

( whereas the number is a rational number if it could be expressed in the form of p/q where p is a integer and  q is a rational number.

Also, the decimal expansion of a number is terminating and repeating )

Ques 1)

A)

$-\sqrt{16}$

We know that this number could also be represented by:

$-\sqrt{16}=-4$

i.e. the number is a rational number since, it is represented in the form of p/q where p= -4 and q=1

B)

$\sqrt{0.4}$

On further simplifying

$\sqrt{0.4}=\sqrt{\dfrac{4}{10}}\\\\\\i.e.\\\\\sqrt{0.4}=\sqrt{\dfrac{2}{5}}\\\\i.e.\\\\\\\sqrt{0.4}=\dfrac{\sqrt{2}}{\sqrt{5}}$

Hence, the number could not be expressed in the form of p/q

Hence, it is a irrational number.

C)

$\sqrt{4}$

It could be represented as:

$\sqrt{4}=2$

i.e. it is a rational number.

Since p= 2 and q=1

D)

$\sqrt{16}$

We know that this number could also be represented by:

$\sqrt{16}=4$

i.e. the number is a rational number since, it is represented in the form of p/q where p= 4 and q=1

Hence, the correct answer is: Option: B

           B)   $\sqrt{0.4}$

Ques 2)

A)

Since, the decimal expansion is a repeating decimal since there is a bar over 8.

Hence, the number is a rational number.

B)

$\sqrt{25}$

It could also be written as:

$\sqrt{25}=5$

Since, the number is in the form of p/q where p=5 and q=1

Hence, the number is a rational number.

C)

$25.8125$

The decimal expansion is terminating.

Hence, the number is a rational number.

D)

$\sqrt{0.025}$

It could also be written by:

$\sqrt{0.025}=\sqrt{\dfrac{25}{1000}}\\\\\\i.e.\\\\\\\sqrt{0.025}=\sqrt{\dfrac{1}{40}}\\\\\\i.e.\\\\\\\sqrt{0.025}=\dfrac{1}{2\sqrt{10}}$

Since, the number does  satisfy the definition of irrational number i.e. it could not be represented in the form of p/q where p is a integer and q is a natural number.

Hence, we get:

The number is a irrational number.