Question

please answer fast.​

Answer 1

Step-by-step explanation:

√3 is a irrational number

2 is rational no.

5 is rational no.

if we multiply a rational with irrational then outcome is irrational

then; 5*√3 is irrational

therefore 2+ 5√3 is irrational (because sum of rational and irrational is alwaus irrational

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Answer 2

Step-by-step explanation:

Let

$2 + 5 \sqrt{3} = a$

♤where a is a rational number..

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

♤ Which is a contradiction as LHS is irrational and RHS Is rational...

=

$2 + 5 \sqrt{3} can \: not \: be \: rational$

Hence

$2 + 5 \sqrt{3} \: is \: irrational$

Alternate method.:::

Let

$2 + 5 \sqrt{3} \: be \: rational$

2+5=p/q p/q are integers q is unequal to 0

$\sqrt{3}$

$\sqrt{3} = { \frac{p}{q - 2} } \div 5$

$\sqrt{3} = \frac{p - 2q}{5}$

LHS Is irrational and RHS is rational which Is a contradiction...

Hence Proved.....