Question

What are the irrational numbers between 2 and 3

Answer 1

Step-by-step explanation:

Hence √7, 3√17, 4√54 and 5√178 are all irrational numbers between 2 and 3, as 4<7<9; 8<17<27; 16<54<81 and 32<178<243.

Answer 2

Answer:

Irrational numbers are numbers that can not be represented in the form of pq

. The square roots and cube roots of most numbers are irrational. Use this to find the irrational numbers between 2 and 3.

Complete step-by-step answer:

Irrational numbers and rational numbers belong to the bigger domain of real numbers.

Rational numbers are numbers that can be represented in the form of pq

where q≠0

.

Irrational numbers are numbers that can not be represented in the form of pq

. Irrational numbers are non-recurring and non-terminating decimal numbers. The square roots of non-perfect square numbers are all irrational and the cube roots of non-perfect cubes are also irrational and so on.

Few examples of irrational numbers are π

, 2–√

, 7–√3

and so on.

In this question, we need to find at least two irrational numbers between 2 and 3. We use the fact that the square root of non-perfect squares is irrational to solve it.

We know that the value of the square of 2 is 4 and the value of the square of 3 is 9.

We choose two numbers between 4 and 9, let's say 6 and 7. Then, we have the following:

4<6<9

4<7<9

Taking square root on all the three terms in each inequality, we get:

4–√<6–√<9–√

4–√<7–√<9–√

Simplifying the above expressions, we get:

2<6–√<3

2<7–√<3

Hence, the two irrational numbers between 2 and 3 are 6–√

and 7–√

.

Note: There are infinite irrational numbers between two rational numbers. Hence, you can obtain as many irrational numbers as you want between the numbers 2 and 3. The answer is just one among them.

So any five irrational numbers between 2√5 and 3√3 are : √21, √22, √23, √24, and √26.