Question

prove 3+2 root3 is irrational

Answer 1

(3+2√3) is an irrational number.

What is irrational numbers with examples?

• An irrational number is a type of real number which cannot be represented as a simple fraction.
• It cannot be expressed in the form of a ratio.
• If N is irrational, then N is not equal to p/q where p and q are integers and q is not equal to 0.
• Example: √2, √3, √5, √11, √21, π(Pi) are all irrational.

According to the question:

Given: Number = 3+2√3.

Let (3+2√3) be a rational number which can be expressed in the form of p/q where p and q have no other common factor than 1.

$3+2 \sqrt{3}=\frac{p}{q}$

$2 \sqrt{3}=\frac{p}{q}-3$

$2 \sqrt{3}=\frac{p-3 q}{q}$

$\sqrt{3}=\frac{p-3 q}{2 q}$

(p-3q)/2q is rational but √3 is irrational.

Thus our contradiction is wrong.

Hence, (3+2√3) is an irrational number.

Learn more about irrational number here,

https://brainly.in/question/2612214?msp_poc_exp=5

#SPJ2