Question

prove that root7 + root13 is irrational​

Answer 1

We can prove that √7 + √13 is irrational number. As;

$\sqrt{7} = 2.6457513111...$

And,

$\sqrt{13} = 3.6055512755...$

Thus, addition of the two numbers, 2.6457513111 and 3.6055512755 will,

${2.6457513111 + 3.6055512755 = 6.2513025865...}$

• Hence, here we can see that, 6.2513025865 is a non-terminating number. And irrational numbers are always non-terminating, hence, √7 + √13 is irrational.