Question

Show that 5+ √3 is irrational.​

Answer 1

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Answer 2

“We have to prove 5 + √3 is irrational”

Let us assume that, 5 + √3 be a rational number.

As we know,

Rational numbers are the numbers that can be expressed in the form of a/b of two integers, where a is the numerator and b ≠ 0.

Now,

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

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

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

In the Above expression,

√3 is irrational, whereas $\frac{a - 5b}{b}$ is rational.

Since, Irrational ≠ Rational

It contradicts the fact that our assumption was incorrect.

Hence, 5 + √3 is irrational.

Hence verified.

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