Question

Please help me with this ques.
Show that 5+√3 is irrational.

Answer 1

if possible let 5+root 3 is a rational number.Also let 'a' and 'b' two positive integers having no common factor other than one

Then, see the attachmebt for better understanding

hope it helps

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Answer 2

Step-by-step explanation:

Let us assume that

$5 + \sqrt{3}$

is a rational number

Now,

it can be written in the form of a/b

$\frac{a}{b} = 5 + \sqrt{3}$

then rearrange it we get

$a = b(5 + \sqrt{3} ) = 5b + \sqrt{3} b$

Now square on both sides

${a}^{2} = (5b + \sqrt{3} b) {}^{2} \\ a {}^{2} = 25b {}^{2} + 10 \sqrt{3} b {}^{2} + 3 {b}^{2}$

but this fact that

$\sqrt{3}$

is irrational

hence our assumption is wrong

we conclude that 5 + √3 is irrational