Prove that 5 3 7 root 3 is irrational

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Proof that 5 minus 3 by 7 root 3 is irrational rational number

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5-\frac{3}{7\sqrt{3}} is an irrational number.

Step-by-step explanation:

To proof : 5-\frac{3}{7\sqrt{3}} is a irrational number ?

Proof :

Let us assume that,

5-\frac{3}{7\sqrt{3}} is a rational number.

Then it can be written in p/q form where p and q are co-prime.

\frac{3}{7\sqrt{3}}=5-\frac{p}{q}

\frac{3}{7\sqrt{3}}=\frac{5q-p}{q}

\frac{3q}{5q-p}=7\sqrt{3}

\frac{3q}{7(5q-p)}=\sqrt{3}

Here, 7,5,3,q,and p are integers.

i.e. LHS is rational number.

We know, \sqrt{3} is an irrational number.

A rational number cannot be equal to irrational number.

This contradict the assumption.

Therefore, 5-\frac{3}{7\sqrt{3}} is an irrational number.

#Learn more

Prove that 5-2/7 root3 is irrational

brainly.in/question/328699


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