Question

prove that 2√5-3 is irrational​

Answer 1

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prove that 2√5-3 is irrational

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Let us assume that 2√5-3 is an irrational number then we can write in the form of p/q, where p&q are co-primes and q is not equal too 0

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$\orange{2√5-3=\frac{p}{q}}$

$\orange{2√5=\frac{p}{q}+3}$

$\orange{√5=\frac{p}{q}+\frac{3}{2}}$

$\orange{√5=\frac{2p + 3q} {q + 2}}$

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$\purple{Hence,}\orange{\frac{2p \times 3q}{q \times 2}} \: \purple{is \: an \: rational \: number}$

$\purple{But ,we \: know \: that \: √5 \: is \: an \: irrational \: number}$

$\purple{Therefore, }\orange{2√5-3 \: }\purple{ is \: not \: an \: rational \: number}$

$\purple{Hence, }\orange{2√5 - 3 \: }\purple{ is \: an \: irrational \: number}$

[Hope this helps you.../]