Math, asked by sumeena, 9 months ago

prove that 2-3√5 is an irrational number

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Answered by Anonymous

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let us assume that 2-3√5is an rational number

so ,

it can be shown in the form of

$\frac{p}{q}$

$2 - 3 \sqrt{5} = \frac{a}{b}$

where a and b are co -prime.

$2 - 3 \sqrt{5} = \frac{a}{b} \\ \\ - 3 \sqrt{5} = \frac{a}{b } - 2 \\ \\ - 3 \sqrt{5} = \frac{a - 2b}{b} \\ \\ \sqrt{5} = \frac{a - 2b}{3b}$

so ,

we know that √5 is irrational and this is equals to to an rational number

so ,

this contradiction is arissen because of our wrong assumption.

so,2-3√5is an irrational number

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