Question

prove that 4-5√3 is an irrational number
​

Answer 1

☞Root 3 in this no. is irrational so 4-5 root 3 is a irrational no.

HOPES, IT'S HELPFUL.

Answer 2

Answer:

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

Step-by-step explanation:

Or

Let us assume that 4−5

3

be rational

⟹4−5

3

=

b

a

where a,bϵZ

⟹−5

3

=

b

a

−4

⟹

3

=

5

4

−

b

a

L.H.S = irrational number as

3

is a irrational number.

R.H.S = rational number

as RHS



=LHS

Hence, our assumption is wrong and 4−5

3

is a irrational number.

U can use any of this procees