Question

Prove that 2 + 5✓3 is irrational number.​

Answer 1

Answer

Ok bro, imma make it as simple as possible.

Let us assume that 2 + 5✓3 is a rational number, (given ✓3 is irrational)

This means that 2 + 5✓3 = a/b, where a and b are coprime integers

Shifting 2 to the RHS,

5✓3 = a/b -2

5✓3 = (a-2b)/b

Shifting 5 to the RHS,

✓3 = (a-2b)/5b

From the above, we infer that a,  -2b and 5b are all integers.

Hence, (a-2b)/5b is rational.

That means, ✓3 is also rational.

This contradicts the fact that ✓3 is irrational.

Therefore, 2 + 5✓3 is irrational.

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Answer 2

Answer:

let us assume that 2+5√3 is a ratinal no.

2+5√3=p/q. (pand q are integers ,qis not equal to

0 )

5√3=p-2q/q

√3=p-2q/5q

p-2q/5q is a rational no.

√3 must be a rational no.

but it is impossible because √3 is an irrational no.

hence,our assumption is wrong

therefore,2+5√3 is an irrational no.

hope it helps u !!

please mark as brainliest !!