Question

03. Find two irrational numbers between 2 and 2.5.​

Answer 1

If a and b are any two distinct positive rational numbers such that ab is not  

a perfect square , then the irrational number √ab lies between a and b.  

∴ Irrational number between 2 and 2.5 is √ 2 × 2.5 , i.e √5  

Irrational number between 2 and √5  is √2 × √5 = 2(1/2) × 5(1/4)  

Irrational number between √5 and 2.5 is √√5 × 2.5 =

Thus the three irrational numbers between 2 and 2.5 are √5  , 2(1/2)  × 5(1/4) and (1/2) × 5 3/4 ×  21/2 .

Answer 2

Answer:

Two irrational numbers between 2 and 2.5 are $\sqrt{5}$and ${2}^{ \frac{1}{2} } \times {5}^{ \frac{1}{4} }$

Step-by-step explanation:

An irrational number is a real number that can not be expressed as an integer ratio, such as √2, is an example of an irrational number. Also, neither ending nor recurring is the decimal expansion of an irrational number. The real numbers that can not be represented in p/q form are recognized as irrational numbers, where p and q are integers and q is not equal to zero.

Examples of irrational numbers are √2 and √3. However, any number in the form of p/q can be represented, p and q are integers and q s not equal to zero is regarded as a rational number.

Pi (π) is an irrational number because it is non-terminating. The approximate value of pi is 22/7 or 3.14…

Consider a and b are two distinct positive rational numbers which is not a perfect square. The irrational number √ab lies between a and b.

∴ Irrational number between 2 and 2.5 is

$\sqrt{2} × 2.5$

i.e. $\sqrt{5}$

Irrational number between 2 and $\sqrt{5}$is $\sqrt{2} \times \sqrt{5}$

Thus the two irrational numbers between 2 and 2.5 are $\sqrt{5}$ and ${2}^{ \frac{1}{2} } \times {5}^{ \frac{1}{4} }$