Question

prove that 5+2√3 is an irrational number​

Answer 1

5 + 2√3 is irrational number

__________ [PROVE]

Solution:

• Let us assume that 5 + 2√3 is irrational number.

=> 5 + 2√3 = $\dfrac{a}{b}$

Here, a and b are co-prime numbers.

=> 2√3 = $\dfrac{a}{b}$ - 5

=> 2√3 = $\dfrac{a\:-\:5b}{b}$

=> √3 = $\dfrac{a\:-\:5b}{2b}$

Here;

$\dfrac{a\:-\:5b}{2b}$

is rational number.

So, √3 is also a rational number.

But we know that √3 is irrational number.

So, our assumption is wrong.

5 + 2√3 is irrational number.

Hence, proved.

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