Question

Prove this is irrational ? 1/√5 - √3

Answer 1

Answer::) hope u mark this as the brainiest

Step-by-step explanation:

given 1/5+√3 is a irrational number

1/5+√3=1/5+√3= p/q

√3=p/q=1/5

√3=(5p-q)/5q

(5p-q)/5q

;;;; it is a rational number

we have to prove it is irrational

now, √3 is a rational

but 1/5+√3 is a irrational number

hence proved

Answer 2

$\Large \fbox \red {Question \: :}$

Prove this is irrational :

$\frac{1}{ \sqrt{5 \: } - \sqrt{3} }$

$\Large \fbox \red {Answer \: :}$

• First we have to rationalise it.

$= \frac{1}{ \sqrt{5} - \sqrt{3} } \times \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} + \sqrt{3} }$

$= \frac{ \sqrt{5} + \sqrt{3} }{( \sqrt{5}) {}^{2} - ( \sqrt{3} ){}^{2} }$

$= \frac{ \sqrt{5} + \sqrt{3} }{5 - 3}$

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

• We can see that the fraction is still in the root form.

We know that,

$\implies$ Irrational ÷ Rational = Irrational

Hence, we can say that this fraction is irrational.

$\implies$ $\mathcal \purple {PROVED!! }$

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