Question

Prove that 2√3 / 5 is irrational

Answer 1

Answer:

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10th

Maths

Real Numbers

Revisiting Irrational Numbers

Prove that 2 - 3 √(5) is an...

MATHS

Prove that 2−3

5

is an irrational no.

EASY

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ANSWER

Let x=2−3

5

be a rational number.

3

5

=2−x

5

=

3

2−x

Since x is rational, 2-x is rational and hence

3

2−x

is also rational number

⇒

5

is a rational numbers, which is a contradiction.

Hence 2−3

5

must be an irrational number.

Answer 2

Answer:

Let x=2−3

5

be a rational number.

3

5

=2−x

5

=

3

2−x

Since x is rational, 2-x is rational and hence

3

2−x

is also rational number

⇒

5

is a rational numbers, which is a contradiction.

Hence 2−3

5

must be an irrational number.

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