Question

prove that 5-√3 is irrational​

Answer 1

AnsWer:-

→Let 5-√3=Rational

→5-√3=$\frac{a}{b}$

[°•°a and b are co-prime integers, a&b≠0]

→5-√3=$\frac{a}{b}$

→-√3=$\frac{a}{b}$-5

★Cross Multiply RHS★

→-√3=$\frac{a-5b}{b}$

→√3=-($\frac{a-5b}{b}$)

→√3=$\frac{-a+5b}{b}$

$\rule{200}{1}$

→√3=Irrational

→$\frac{-a+5b}{b}$=Rational

=>As LHS≠RHS,also Irrational≠Rational,This thus Creates Contradiction and Proves 5-√3 is Irrational.

$\rule{200}{2}$

Answer 2

Answer:

5-√3 is irrational

Step-by-step explanation:

We have to prove 5-√3 is irrational.

Let us assume the opposite

i.e. 5-√3 is rational.

Therefore, 5-√3 can be written in the form of a/b

where b is not equal to 0.

hence, 5-√3= a/b

= -√3 = a/b -5

= -√3 = a-5b/b

= √3 = -(a-5b/b)

√3 is irrational and 5b-a/b is rational.

Since rational is not equal to irrational,

5-√3 is irrational.

Therefore, our assumption is incorrect