Question

show that 6+5 root 3 is irrational​

Answer 1

Step-by-step explanation:

To prove that it is irrational number,

Let us think that 6+5√3 is a rational number.

so,

6+5√3 can be written as p/q, because every rational number can be written as p/q. so

6+5√3 = p/q

=> 11√3 = p/q

=> 11×√3 = p/q

=> √3 = p/q÷11

=> √3 = p/q×1/11

=> √3 = p/11q

Here p/11q is rational number but we know that √3 is an irrational number, so our assumption was wrong. And 6+5√3 is an irrational number. It is proved.

hope it helps.