# Prove that 7√5 Is Irrational Number

By BYJU'S Exam Prep

Updated on: September 25th, 2023

An irrational number cannot be stated using fractions, but a rational number may be expressed as the ratio of two integers with the denominator not equal to zero. Irrational numbers do not have terminating decimals, whereas rational numbers do.

Assume for the moment that 7√5 is a rational number.

Therefore, 7√5 can be expressed as a/b, where a, b are co-prime numbers and b is not equal to 0.

7√5 = a/b

√5 =a/7b

Here, √5 is an irrational number but a/7b is a reasonable one.

Rational number ≠ Irrational number

It runs counter to our belief that 75 is a rational number.

### How to Know if a Number is Irrational?

Irrational numbers are real numbers that cannot be represented in the form of p/q, where p and q are integers and q ≠ 0. For instance, √2 and √ 3 are so forth, are irrational. However, any number that can be expressed as p/q, where p and q are integers and q ≠ 0, is to as a rational number.

Therefore, 7√5 is an irrational number.

Summary:-

## Prove that 7√5 Is Irrational Number

It is proved that 7√5 is irrational number. Irrational numbers are real numbers that cannot be represented in the form of p/q, where p and q are integers and q ≠ 0. The famous irrational numbers consist of Pi, Euler’s number, and Golden ratio.

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