Question

Find there rational numbers and
three irrational numbers between 4 and 5​

Answer 1

Answer:

you have the irrational square roots (as has been mentioned in other answers). 4 is the square root of 16, and 5 is the square root of 25, so the square root of any number between 16 and 25 (could be an integer, but doesn’t have to be) is irrational.

meanwhile, numbers like pi, e and the golden ratio φ (all irrational) can be multiplied by certain numbers, which will give a product between 4 and 5, but still irrational.

φ (the golden ratio) starts off as 1.618…

multiplying 1.6 by 3 gives 4.8.

multiplying 1.618… by 3 gives 4.854…

hence, 3φ is between 4 and 5, and is irrational.

e = 2.718…

multiplying this by, say, 1.5 gives 4.077…

hence, 1.5e is between 4 and 5, and is irrational.

hope this helped!

Answer 2

Answer:

Rational no.

$= \frac{4}{1} \: \: \: \:and \: \: \: \: \: \frac{5}{1} \\ = \frac{4 \times 5}{1 \times 5} \: \: \: and \: \: \: \frac{5 \times 5}{1 \times 5} \\ = \frac{20}{5} \: \: and \: \: \frac{25}{5 } \\ = < three \: rational \: no \: are > \\ = \frac{21}{5} \: and \: \frac{22}{5} \: and \: \frac{23}{5}$

Irrational no.

• 4
• 5
• so, irrational no. between 4 and 5 are=>
• 4.12345..............
• 4.9234...............
• 4.54678.............