prove that under root 5 is irrational

1.	prove that under root 5 is irrational
Answer» To show that √5 is an irrational number, we will assume that it is rational Then, we need to find a contradiction when we make this assumption If we are going to assume that √5 is rational, then we need to understand what it means for a number to be rational Basically, if square root of 5 is rational, it can be written as the ratio of two numbers as shown below: Square both sides of the equation above 5 = x2y2 Multiply both sides by y2 5 × y2 = x2y2 × y2 We get 5 × y2 = x2

Answer»

To show that √5 is an irrational number, we will assume that it is rational

Then, we need to find a contradiction when we make this assumption

If we are going to assume that √5 is rational, then we need to understand what it means for a number to be rational

Basically, if square root of 5 is rational, it can be written as the ratio of two numbers as shown below:

Square both sides of the equation above

5 = x2y2

Multiply both sides by y2

5 × y2 = x2y2 × y2

We get 5 × y2 = x2

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