Question

Prove that √6 is irrational.

Answer 1

Answer:

Prove That Root 6 is Irrational by Contradiction Method

If k was a prime number and k divides a2 evenly, then k also divides 'a' evenly, where a is any positive integer. Hence the equation (2) shows 6 is a factor of p2 which implies that 6 is a factor of p. ... Thus, the square root of 6 is irrational.

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Answer 2

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Prove That Root 6 is Irrational Number

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Is root 6 an irrational number? Mathematically, a number that is represented in p/q form where p and q both are integers, and q is not equal to 0, is referred to as a rational number whereas the number that cannot be represented in p/q form are called irrational numbers. A number whose decimal expansion keeps extending after the decimal point is also categorized as an irrational number. Now let us take a look at the detailed discussion and prove that root 6 is irrational.

Prove That Root 6 is Irrational Number

Problem statement: Prove that root 6 is an irrational number

Proof: When we calculate the value of √6, we get √6 = 2.449489742783178... It is a decimal number that does not terminate and terms are not repeating themselves after the decimal point. Thus, the value obtained for the root of 6 satisfies the condition of being a non-terminating and non-repeating decimal number that keeps extending further after the decimal point which makes √6 an irrational number.

Hence, √6 is an irrational number.

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