Question

Prove that √5+√7 is an
irrational number.
​

Answer 1

Answer:

first you prove √5 is a n irrational number

similarly, √7 is also an irrational number

therefore, its sum is also irrational.

Answer 2

To Prove : Let $x=\sqrt{5} +\sqrt{7}$ and use rational zero thm.

Square both sides

$x^2=12+2\sqrt{35}$

Isolate radical, square again

$x^4-24x^2+144=140$

Simplifying the equation, we get

$x^4-24x+4=0$

By the rational zero thm, the possible rational zeros are

Possible Zeros : $\frac{\pm4}{\pm1} =4,-4,1,-1$

None of the followings are zeros.

We can conclude that the equation has no rational zeros.

Therefore, $\sqrt{5} +\sqrt{7}$ is not rational.

Hence proved.

If you don't understand then watch BlackPenRedPen's video on YouTube.

Can you give me a brainliest :(