Question

prove that it is irrational
$7 \sqrt{5}$
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Answer 1

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Answer 2

ANSWER:

• 7√5 is an irrational number.

GIVEN:

• Number = 7√5

TO PROVE:

• 7√5 is an irrational number.

SOLUTION:

Let 7√5 be a rational number which can be expressed in the form of p/q where p and q have no other common factor than 1.

$\implies \: 7 \sqrt{5} = \dfrac{p}{q} \\ \\ \implies \: \sqrt{5} = \dfrac{p}{q} \times \frac{1}{7} \\ \\ \implies \: \sqrt{5} = \dfrac{p}{7q}$

• Here p/7q is rational but √5 is Irrational.
• Thus our contradiction is wrong.
• So 7√5 is an irrational.

NOTE:

• This method of proving and irrational number is called contradiction method.
• In this method we first contradict a fact than we prove that our contradiction was wrong.