Below are the steps with respect to proving -2 as an irrational number- Choose the correct order of the steps-

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Mathematics

Sqrt(P) Is Irrational, When 'P' Is a Prime

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Question

Below are the steps with respect to proving $\sqrt{2}$ as an irrational number. Choose the correct order of the steps.

1, 2, 3

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2, 1, 3

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2, 3, 1

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3, 2, 1

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Solution

The correct option is C 2, 3, 1

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Similar questions

Q. To prove

\sqrt{2}

as an irrational number-

(i) We assume

\sqrt{2} = \frac{a}{b}, (b \neq 0)

such that a and b are co-primes.

(ii) On simplifying, we get 2 divides a, which results in contradiction.
Which of the above two statements is/are correct?

Q. Fill in the blanks to complete the proof of

2 - \sqrt{5}

as an irrational number, provided

\sqrt{3}

is an irrational number.

Let’s assume

2 - \sqrt{5}

be a rational number

\Rightarrow 2 - \sqrt{5} = \frac{a}{b}, b \neq 0

\Rightarrow \sqrt{5} =

(i)___________ which is a (ii)_________ number.

\Rightarrow \sqrt{5}

is a rational number.
But

\sqrt{5}

is an irrational number.
Hence, we have arrived at a contradiction.

∵ 2 - \sqrt{5}

is an irrational number.

Q. Fill in the blanks to complete the proof of

2 \sqrt{5}

as an irrational number, provided

\sqrt{5}

is an irrational number.

Let’s assume

2 \sqrt{5}

be a rational number

2 \sqrt{5} = \frac{a}{b}, b \neq 0

\Rightarrow \sqrt{5} =

(i)___________ which is a (ii)_________ number.

\Rightarrow \sqrt{5}

is a rational number.
But

\sqrt{5}

is an irrational number.
Hence, we have arrived at a contradiction.

∵ 2 \sqrt{5}

is an irrational number.

Q. Fill in the blanks to complete the proof of

1 + 7 \sqrt{3}

as an irrational number, provided

\sqrt{3}

is an irrational number.

Let’s assume

1 + 7 \sqrt{3}

be a rational number

\Rightarrow 1 + 7 \sqrt{3} = \frac{a}{b}, b \neq 0

\Rightarrow \sqrt{3} =

(i)___________ which is a (ii)_________ number.

\Rightarrow \sqrt{3}

is a rational number.
But

\sqrt{3}

is a/an irrational number.
Hence, we have arrived at a contradiction.

∵ 1 + 7 \sqrt{3}

is an irrational number.

If a, b, c are rational numbers such that a² + b² + c² − ab − bc − ca = 0, prove that a = b = c.

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Below are the steps with respect to proving √2 as an irrational number. Choose the correct order of the steps.

The correct option is C 2, 3, 1

Below are the steps with respect to proving $\sqrt{2}$ as an irrational number. Choose the correct order of the steps.