Question

Find 3 irrational number between 1 /2 and 1/3​

Answer 1

Answer: 0.3333 and 0.5.

Step-by-step explanation: by using the formula (a+b/2) we can find rational numbers between any two rational numbers .we can take "a" as the first rational number and "b" as the second rational number

Answer 2

Concept

An irrational number is a number that cannot be represented in the form p/q, where p and q are integers, q is not equal to 0, and p and q are co-prime to each other.

Given

Two numbers: 1/2 and 1/3

Find

We are asked to find three irrational numbers between 1/2 and 1/3.

Solution

We follow the following steps to find irrational numbers between 1/2 and 1/3.

We know,

1/3 < 1/2

or, √((1/3)²) < √((1/2)²

or, √(1/9) < √(1/4).

Now, we can also write that:

√(1/9) < √(1/8) < √(1/7) < √(1/6) < √(1/5) < √(1/4)

And we know that √(1/8), √(1/7), √(1/6), and √(1/5) are irrational numbers as they cannot be written in the form of p/q, where p and q are integers, q is not equal to zero, and p and q being co-prime to each other.

Thus, we can write any 3 among these 4.

3 irrational numbers between 1/2 and 1/3 are √(1/8), √(1/7), and √(1/5).

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