Question

prove that square root of 5+square root of 7 is an irrational number
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Answer 1

Answer:

be rational, and let p/q are co-prime where q is not equal to zero (0). We know that is irrational while p/q form is rational. Hence it contradicts our assumption of is rational. Hence, it is proved that is irrational.

Answer 2

To prove:-

To prove that √5 +√7 is an irrational number or not

Solution:-

Let us assume that

√5 + √7 be rational number and let p/q ate co-prime where q is not equal to zero (0)

$\sqrt{5} + \sqrt{7} = \frac{p}{q}$

$\sqrt{5} = \frac{p}{q} - \sqrt{ 7}$

$\sqrt{5} = \frac{p - \sqrt{7 \: q} }{ q}$

We know that √5 is irrational no. while p/q form is rational.

Hence, it contradicts our Assumption of

√5 +√7 is rational.

Hence it is proved that √5 + √7 is irrational!