Question

prove that 6-2 root3 is irrational

Answer 1

Answer:

6-2root 3

Step-by-step explanation:

bhai phle root 3 ko irrational prove kr de NCERT me bhi h ye

uske bad

6-2root3 ko rational man le

6-2root3 = p/q

to fir 2root3 = 6+p/q

to fir 2 ko vaha divide m le ja uske bad likh de root 3 is irrational we proved above but 6+p/q is rational amd rational and irrational does not equal to each other so 6-2root3 is irrational

Answer 2

Answer:

$Let\:us \: suppose \: 6 - 2\sqrt{3} \: is \: rational$

$Let \: 6 - 2\sqrt{3} = \frac{a}{b} \\ ( a,b \: are \: integers \:and \: a ≠ 0 )$

$-2\sqrt{3} = \frac{a}{b} - 6$

$\implies -2\sqrt{3} = \frac{a - 6b}{b}$

$\implies \sqrt{3} = \frac{a - 6b}{-2b}$

$Since , a,b \: are \: integers ,\: So,\frac{a - 6b}{-2b} \: is \\ rational \: number, \: Hence,\: \sqrt{3} \: rational \: number .$

$It \: is \: contradiction .$

Therefore.,

$6 - 2\sqrt{3} \: is \: irrational \: number$

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