Question

Show that 2√5 is an irrational number.​

Answer 1

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Answer 2

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Class 10

>>Maths

>>Real Numbers

>>Revisiting Irrational Numbers

>>Prove that 2 + √(5) is an irrational num

Question

Prove that 2+

5

is an irrational number.

Easy

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Solution

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If possible, let us assume 2+

5

is a rational number.

2+

5

=

q

p

where p,q∈z,q



=0

2−

q

p

=−

5

q

2q−p

=−

5

⇒−

5

is a rational number

∵

q

2q−p

is a rational number

But −

5

is not a rational number.

∴ Our supposition 2+

5

is a rational number is wrong.

⇒2+

5

is an irrational number.