Question

Prove that 7-2 root 3 or 7+3 root 2 is an irrational number

Answer 1

Answer:

Given- 7-2√3 is a number. = To prove that 7-2√3 is an irrational number.

Step-by-step explanation:

Let us assume that it is a rational number so there must be co-primes "a" and "b" such that :-. 7-2√3 = a/b , then => -2√3= a/b + 7, => -2√3= a+7b/b , => √3= a+7b/-2b. Now we got that a+7b/-2b is a rational number so √3 is also a rational number. But this contradicts the fact that √3 is irrational , so our assumption is wrong then it is proved that 7-2√3 is a irrational number. similarly you can do the next number.

Answer 2

Answer:Answer:

Given- 7-2√3 is a number. = To prove that 7-2√3 is an irrational number.

Step-by-step explanation:

Let us assume that it is a rational number so there must be co-primes "a" and "b" such that :-. 7-2√3 = a/b , then => -2√3= a/b + 7, => -2√3= a+7b/b , => √3= a+7b/-2b. Now we got that a+7b/-2b is a rational number so √3 is also a rational number. But this contradicts the fact that √3 is irrational , so our assumption is wrong then it is proved that 7-2√3 is a irrational number. similarly you can do the next number.

Step-by-step explanation: