Question

An irrational number between 3 and 4 is ______.

Options

• 3.1112003

• `sqrt(20)`

• `sqrt(10)`

• 3.142

Answer 1

An irrational number between 3 and 4 is `underlinebb(sqrt(10))`.

Explanation:

a. 3.1112003

This is a decimal number that terminates, so it is rational, not irrational.

b. `sqrt(20) = sqrt(4 xx 5) = 2sqrt(5)`

Since `sqrt(5)` is irrational, `2sqrt(5)` is irrational.

Also, `sqrt(20) ≈ 4.472`, which is greater than 4, so not between 3 and 4.

c. `sqrt(10) ≈ 3.162`

This lies between 3 and 4 and it is irrational.

d. 3.142

This is a terminating decimal approximation of π, so 3.142 is rational (though π itself is irrational).