Question

Prove that ✓5is irrational

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Step-by-step explanation:

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:

√5=x/y.

Square both sides of the equation above:

5=x2/y2

Multiply both sides by y2

5 × y2 =x2/y2 x y2

We get 5 × y2 = x2

In order to prove that square root of 5 is irrational, you need to understand alThis is a contradiction since a number cannot have an odd number of prime factors and an even number of prime factors at the same time

The assumption that square root of 5 is rational is wrong. Therefore, square of 5 is irrationalso this important concept.

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