## anonymous 4 years ago What is the square root of 3?

1. anonymous

2. anonymous

Go away

3. ParthKohli

The square root of three is an irrational number. Its approximation is 1.73205......(as I said, it never ends. That is the reason that it is irrational)

4. ParthKohli

I can prove that $$\sqrt3$$ is irrational. First assume that $$\sqrt3$$ is rational. As per the definition of rational numbers, a rational number is the division of two co-prime integers $$p$$ and $$q$$. $$\color{Black}{\Rightarrow {\Large {p\over q}} = \sqrt3}$$ Squaring both sides: $$\color{Black}{\Rightarrow \Large {p^2 \over q^2} \normalsize = 3}$$ Multiply both sides by $$q^2$$. $$\color{Black}{\Rightarrow q^2 = 3p^2}$$ Continue from here ;)

5. karatechopper