Question

Which number is an irrational number? StartFraction negative 22 Over 9 EndFraction Negative StartRoot 3 EndRoot 2.56 StartRoot 15 EndRoot

Answer 1

Answer:

Option B and Option D

Step-by-step explanation:

Irrational number: The numbers which cannot write as proper or improper fraction.

If we write as decimal then it would be non terminating and non repeating decimal.

Option A)

$-\dfrac{22}{9}$

Using calculator write fraction as decimal.

Therefore, $-\dfrac{22}{9}=2.4444......\approx 2.\bar{4}$

It is repeating decimal number. It won't be irrational number.

Option B)

$-\sqrt{3}$

It is radical number. Radical number is always irrational number.

It would be irrational number.

Option C)

2.56

It is terminating decimal number. So, it can be write as fraction.

It won't be irrational number.

Option D)

$\sqrt{15}$

It is radical number. Radical number is always irrational number.

It would be irrational number.

Hence, $-\sqrt{3}$ and $\sqrt{15}$ are irrational number.

Answer 2

Answer:

Option 2 and 4.        

Step-by-step explanation:

To find : Which number is an irrational number?

Solution :

An irrational number is defined as the number which cannot be expressed in p/q form where p and q are integers and q is non-zero.

Irrational number are non-terminating and non-repeating.

1) $-\frac{22}{9}$

$-\frac{22}{9}=-2.44444444444..$

It is non-terminating but repeating.

It is not an irrational number.

2) $-\sqrt3$

$-\sqrt3=-1.73205080757..$

It is non-terminating and non-repeating.

It is an irrational number.

3) $2.56$

$2.56=\frac{256}{100}$

It is a rational number as it is written in p/q form.

It is not an irrational number.

4) $\sqrt{15}$

$\sqrt{15}=3.87298334621..$

It is non-terminating and non-repeating.

It is an irrational number.

Therefore, option 2 and 4 are correct.