Question

Prove that 4+2 root 3 is irrational

Answer 1

Answer:

• let 4-5√3 be a rational number.
• 4-5√3= a/b where a and b are co primes
• -5√3=a/b-4
• -5√3=a-4b/b
• a-4b/b+5=√3
• But this contradiction is wrong therefore 4-5√3 is a irrational number.
• Hope this will help you.
• by the same procedure......

Step-by-step explanation:

Answer 2

let , 4 + 2 √ 3 is a rational no., so it can be written in the form of p/q , where p and q are integers and q not equal to zero.

p / q= 4 + 2 √3

p/ q - 4 = 2√3

p -4q/ q = 2 √3

1/2 ( p -4q / q ) = √3

1/2 (p -4q/ q) is a rational no., as p and q are integers . it means √3 is a rational no. , but we know that √ 3 is irrational. so, 4 +2 √ 3 is irrational.

i hope this will help u and satisfy Ur need.