Question

prove that 8+2 root 3 is irrational number ​

Answer 1

Question:

prove that is 8+2√3 irrational number.

Answer:

let us assume that is 8+2√3 rational.

☆Thus it can be written in the form a/b (b≠0)and A and b are coprime.

$= > 8 + 2 \sqrt{3} = \frac{a}{b} \\ \\ = > 8 - \frac{a}{b} = 2 \sqrt{3} \\ \\ = > \frac{8b - a}{b} = 2\sqrt{3}$

☆since a and b are integers then we get (8b-a)/b is rational number and √3 is also rational number .

☆ but it is not true because √3is irrational.

☆ Therefore the given number 8+2√3is irrational and assumption taken is wrong.

Answer 2

An irrational number is real number that cannot be expressed as a ratio of two integers. When an irrational number is written with a decimal point, the numbers after the decimal point continue infinitely with no repeatable pattern.

The number "pi" or π (3.14159...) is a common example of an irrational number since it has an infinite number of digits after the decimal point. Many square roots are also irrational.

√3 is also irrational number.