Question

prove that 7-root 5 is irrational given that root 5 is irrational​

Answer 1

Answer:

we can find co-primes a and b

7-√5=a/b

7/1-a/b=√5

7b-a/b=√5

7b-a/b=√5 is rational,√7 is also rational.this is our contradiction.this contradiction arise due to our wrong assumption.so7-√5 is irrational number

Answer 2

Answer:

Step-by-step explanation:

let assume (7 - √5) a rational number

∴(7 - √5) = a/b

=> 7 - √5 = a/b

=> √5 = a/b + 7

=> √5 = (a + 7b)/b

as ,here √5 is irrational therefore , whole {(a + 7b)/b} is irrational

∴ 7-√5 is also irrational.

hence proved!

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