Question

prove that 3/root5 is irrational number​

Answer 1

Answer:

a rational number is one that can be represented in the form of p/q where q is not equal to zero and PA and q are both integers and since root 5 is not an integer 3/√5 is not a rational number and is thus irrational.

Answer 2

Concept: The group of real numbers known as irrational numbers are those that cannot be stated as a fraction, p/q, where p and q are integers. (q 0) The denominator is not equal to zero. Additionally, an irrational number's decimal expansion neither repeats nor terminates.

Given:  $3\sqrt5$ is the given number.

Find: Whether $3\sqrt5$ is rational or not.

Solution: Suppose that  $3\sqrt5$  is rational then it is of the form $\dfrac{p}{q}$ where q≠0

and p and q are integers.
But then 3q=p/√5  which shows that 3q is an integer and hence, $\dfrac{p}{\sqrt5}$ is also an integer, which is false. Hence, our assumption was wrong.

Therefore, 3√5 is irrational number.

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