Question

Determine if the square root of 45 is rational or irrational and why

Answer 1

Determine if the square root of 45 is rational or irrational and why

- IRRATIONAL

Why?

The square root of 45 does not constitute a rational number or a real number because it cannot be expressed using the form of p/q.

The two distinct approaches to identify the valuation of the square root of 45 are prime factorization and the long division process.

Answer 2

It is not possible to break 45 into two such factors which, on squaring, give 45. It can be approximately written as a square of 6.708, which is a non-recurring and non-terminating decimal number. This shows that it is not a perfect square, which also proves that the square root of 45 is an irrational number.