Question

1 Rational and 1 irrational number between 2 and root 5

Answer 1

Answer:

Step-by-step explanation:

If we want a rational number = 2<x<√5

it certainly need to satisfy   = 4<x²<5

We can write 4 = 100/ 25 and 5 = 125/ 25,

Also, 11² =121 and  100 < 121 < 125

Thus, it follows - it follows that  4 = 100/25 < 121/25 < 125/25 = 5

such that so that  2 < 11/5 <√5

Since, a non negative rational number has a rational square root if and only if it can be written as the quotient of two integer perfect squares. So, for example,  √120/ 25 and √122/25 are irrational, while still being between 2 and √5.

Thus, between 2 and √5 ≈2.236 we have 2.1 as one rational number and e−7/10 as one irrational number.

Answer 2

Answer:

$Rational \: number \: between \: 2 \: and \: \sqrt{5}\: is \: 2.1$

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

Step-by-step explanation:

$Given \: two \: numbers \: 2 \: and \: \sqrt{5}$

$\sqrt{5}≈2.23606$

$Rational \: number \: between \: 2 \: and \: \sqrt{5}\: is \: 2.1$

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

/* We know that,

Irrational number between a and b is √ab*/

•••♪