Question

Prove that 4 - 2√3 is irrational , given that √3 is irrational number.
​

Answer 1

Step-by-step explanation:

it is given that √3 is irrational number

hence 2√3 is also an irrational number

so,when we add or substact an irrational number from rational number,we get an irrational number

Answer 2

$\huge \bold{ \pink{A} \green{N} \red{S} \blue{W} \purple{E} \orange{R}}$

Let us assume on a contrary that 4 - 2√3 is an irrational number. there exist two numbers a and b such that a ≠ b. where a and b are co-primes.

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: 4 - 2 \sqrt{3} = \frac{a}{b}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: 2 \sqrt{3} = 4 + \frac{a}{b}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: 2 \sqrt{3} = \frac{4b + a}{b}$

we can see that

$\frac{4b + a}{b}$

is in the form of a/b but we know that√3 is an irrational number.

Hence, our assumption is wrong.4 - 2√3 is an irrational number.

$\underbrace\orange{please \: mark \: as \: brainliest............}$