Question

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Show that 3√6 and 3√3 is not a rational number.

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Answer 1

$\large\underline\mathfrak{Question-}$

Show that 3√6 and 3√3 is not a rational number.

$\large\underline\mathfrak{Solution-}$

(i) 3√6

Let a = 3√6 ( where a is rational number. )

•°• a/3 = √6 ......(1)

We know that √6 is an irrational number as it is non terminating as well as non repeating.

Also, if we add, subtract, multiply or divided any non zero rational number with an irrational number, the result is always be irrational.

And any irrational number can't be equal to a rational number.

From (1), it is clear that 3√6 is not a rational number i.e irrational number.

$\rule{300}1$

(ii) 3√3

Let a = 3√3 ( where a is rational number. )

•°• a/3 = √3 ......(1)

We know that √3 is an irrational number as it is non terminating as well as non repeating.

Also, if we add, subtract, multiply or divided any non zero rational number with an irrational number, the result is always be irrational.

And any irrational number can't be equal to a rational number.

From (1), it is clear that 3√3 is not a rational number i.e irrational number.

Hence proved!

Answer 2

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