Question

Prove that 4-5√3 is an irrational number. ​

Answer 1

Answer:

Prove that 4-5 square root 3 is irrational -

Assume that 4 - 5√3 is rational. ...

Because,

the RHS, p²/q² subtracted from 91,

hry is rational, where p²/q² = (p/q)² is rational as it is square of a rational number p/q, but while the LHS, 40√3, is irrational. ∴ 4 - 5√3 is irrational. Hence proved!

Answer 2

Answer:

Assume that 4 - 5√3 is rational.

So that 4 - 5√3 can be written as p/q, where p, q are coprime integers and q ≠ 0.

when solved......

Here it contradicts our earlier assumption that 4 - 5√3 is rational.

Because, the RHS, p²/q² subtracted from 91, is rational, where p²/q² = (p/q)² is rational as it is square of a rational number p/q, but while the LHS, 40√3, is irrational.

∴ 4 - 5√3 is irrational.

Hence proved!

and always remember that the difference of a rational and irrational would be always equal to irrational number only

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