Question

find two rational and two irrational numbers between √5 and √6

class 9 (CBSE board) mathematics

no spammers please​

Answer 1

Step-by-step explanation:

Given :-

Two numbers are √5 and √6

To find :-

Find two rational and two irrational numbers between √5 and √6 ?

Solution :-

Given numbers are √5 and √6

We know that

The irrational number between two numbers a and b is √(ab).

Finding first irrational number between √5 and √6 :-

Let a = √5

Let b = √6

The Irrational number between them

=>√(√5×√6)

=>√√(5×6)

=>√√30 or (30)^1/4

Finding Second irrational number between√5 and √√30:-

Let a = √5

Let b = √√30

The Irrational number between them

=>√(√5×√√30)

=>√[√√(5×5)×√√30]

=> √[√√25×√√30]

=> √[√√(25×30)]

=>√[√√(750)]

=> √√√750 or (750)^1/8

√5, √√√750, √√30 ,√6

Answer:-

The required irrational number between the given two numbers are √√30 or (30)^1/4 and √√√750 or (750)^1/8

Used formulae:-

• The irrational number between two numbers a and b is √(ab)

• √a = a^1/2

• √√a = a^1/4

• √√√a = a^1/8

Points to know :-

• The numbers can not be written in the form of p/q are called Irrational numbers,where p and q are integers and q≠0.

• Irrational numbers are denoted by Q' or S

• √2,√3,..,π,e... are irrational numbers.

• The decimal expansion of the irrational numbers is non terminating and non recurring decimal.