Question

Prove that $5-\cfrac{3}{7\sqrt{3}}$ is an irrational number.

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Answer 1

Answer:

• 5 - 3/(7√3) is an irrational number.

Step-by-step explanation:

Given

• 5 - 3/(7√3)

To find

• To prove that it is a irrational number.

Solution

⇾ Let us assume 5 - 3/(7√3) to be a rational number,

⇾ Then, let's write it in the form p/q,

⇾ 3/(7√3) = 5 - p/q (L.C.M)

⇾ 3/(7√3) = 5q - p/(q) (Cross multiply)

⇾ 3q/(5q - p) = 7√3

⇾ 3q/7(5q - p) = √3

Here the L.H.S is a rational number and R.H.S are integers.

And as we know that a rational number cannot be equal to an irrational number, 5 - 3/(7√3) is an irrational number.

Answer 2

Answer:

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