Math, asked by VεnusVεronίcα, 2 months ago

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

→ Don't spam!
→ Answer with explanation!

Answers

Answered by CopyThat
27

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.

Answered by happyaswal101
10

Answer:

hope it helps you out

plz leave a like

Attachments:
Similar questions