# Thread: Lenght of a vector with square root

1. ## [SOLVED] Lenght of a vector with square root

Hello, how do I find the lenght of a vector when one of the coords is given with a square root, I know that I should use Pythagoras, but I am not sure how to handle it when the vector is given with a square root like this:

Vector a = Square root 4, 8

2. ## Re: Lenght of a vector with square root

Originally Posted by Artifact
Hello, how do I find the lenght of a vector when one of the coords is given with a square root, I know that I should use Pythagoras, but I am not sure how to handle it when the vector is given with a square root like this:
Vector a = Square root 4, 8
If $\vec{v}=(\sqrt{6},\sqrt{3})$ then $\|\vec{v}\|=\sqrt{(\sqrt{6})^2+\sqrt{3})^2}=3.$

3. ## Re: Lenght of a vector with square root

I mean if I have something like this, how do I calc the length of that vector

4. ## Re: Lenght of a vector with square root

Originally Posted by Artifact
I mean if I have something like this, how do I calc the length of that vector
You do the same way.
For any vector $\vec{a}=\left( {\begin{array}{c} p \\ q \\ \end{array} } \right)$, the length $\|\vec{a}\|=\sqrt{p^2+q^2}$.

Square each coordinate, add together, then find the square root.

5. ## Re: Lenght of a vector with square root

Ah ok, thank you very much