Question

prove that 2+5root2 is an irrational number​

Answer 1

Step-by-step explanation:

step 1. let 2+5√2 is rational number than it can be written as a/b where a and b are integer and b is not equal to 0.

step2. 2+5√2 = a/b

5√2 = a/b - 2

5√2 = a -2b/b

√2 = a-2b / 5b

step 3. here we know that a, b,2, and 5 are rational number so the √2 will become rational.

step 4. but this contradicts the fact that √2 is irrational.

so our assumption is wrong that is why 2+5√2 is irrational

Answer 2

Answer:

Step-by-step explanation:

Let us assume to a contarary that 2+5root 2 is a rational number

so, 2+5root2 = a/b

where a and b are co prime numbers and b is not equal to 0

2+5root=a/b

5root2=a/2b

root 2=a/10b

here a,10 and b are integers so

a/10b is a rational number

hence root 2 is also rational

which brings us to a contarary that root 2 is irrational

therefore 2+5root2 is irrational number

HOPE IT HELPS YOU ...........