Question

2. Prove that 2+5√3 is irrational.​

Answer 1

Step-by-step explanation:

▪️Therefore, 2+5√3=a/b (where a and b are co prime)

▪️5√3=a/b-2

▪️5√3=a-2b/b

▪️√3=a-2b/5b

▪️Therefore, a-2b/5b is in the form of a/b which is rational number.

▪️But,this is contradicts the fact is that √3 is irrational number.

▪️Therefore, our assumption is wrong and 2+5√3 is an irrational number.

Therefore, our assumption is wrong and 2+5√3 is an irrational number.Hope this will help you❤️❤️

Answer 2

Answer:

Let, us assume that 2+5√3 is a rational number.

Therefore, 2+5√3=a/b (where a and b are co prime)

5√3=a/b-2

5√3=a-2b/b

√3=a-2b/5b

Therefore, a-2b/5b is in the form of a/b which is rational number.

But,this is contradicts the fact is that √3 is irrational number.

Therefore, our assumption is wrong and 2+5√3 is an irrational number.

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