Question

find two irrational or two rational no.between root 2 amd root 3​

Answer 1

I will go for rational.

1. mean method.

let 2 rationals are x1 and x2.

x1= 2+3/2=5/2.

x2={2+(5/2)}×1/2= 4+5/2×1/2=9/2×1/2= 9/4.

2 irrationals are √5 and √6,8

Answer 2

Solution :—

we know that, if A and B are two distinct positive rational numbers then √ab is an irrational number lying between a and b.

Hence ,

Irrational number between √2 and √3 is :-

$= > \sqrt{ \sqrt{2} \times \sqrt{3} } = \sqrt{ \sqrt{6} } = 6^{ \frac{1}{4} }$

Irrational number between √2 and 6^1/4 is :-

$= > \sqrt{ \sqrt{2} \times \sqrt{6^{ \frac{1}{4} } } } = 2^{ \frac{1}{4} } \times 6^{ \frac{1}{8} }$

Hence , required a rational numbers are :-

$(i) \: 6^{ \frac{1}{4}}$

$(ii) \: 2^{ \frac{1}{4} } \times 6^{ \frac{1}{8} }$