Thursday, September 3, 2015

Prove $\sqrt{2}+\sqrt{3}\gt \pi$

Prove $\sqrt{2}+\sqrt{3}\gt \pi$.

Note that we could use the previously established result from the famous people or even our own finding to construct for the future conjectures and hence argument to help us in determining the plot that we are going to use to solve the new problem at hand, that is one of the very good traits of highly proficient problem solver.

And this problem is the perfect candidate for us to practice using the previously established result in generating the solid proof.

We could use the well-known inequality that says $\dfrac{22}{7}>\pi$ to assist in my method of proving, as shown below:

Note that

$7938>7921$

$2(63)^2>89^2$

$\sqrt{2}>\dfrac{89}{63}$ and

$762048>760384$

$3(504)^2>872^2$

$\sqrt{3}>\dfrac{872}{504}$,

$\therefore \sqrt{2}+\sqrt{3}>\dfrac{22}{7}>\pi$ and we're hence done.