# Expand? (a^2+b^2)^(3/2)

$\left({a}^{2} + {b}^{2}\right) \sqrt{{a}^{2} + {b}^{2}}$

#### Explanation:

${\left({a}^{2} + {b}^{2}\right)}^{\frac{3}{2}}$

The fractional power $\frac{3}{2}$ says that we're going to cube the expression (the 3) and then take the square root (the 2). So let's do that:

$\sqrt{\left({a}^{2} + {b}^{2}\right) \left({a}^{2} + {b}^{2}\right) \left({a}^{2} + {b}^{2}\right)}$

Since $\left({a}^{2} + {b}^{2}\right) \left({a}^{2} + {b}^{2}\right) = {\left({a}^{2} + {b}^{2}\right)}^{2}$, we can write:

$\sqrt{{\left({a}^{2} + {b}^{2}\right)}^{2} \left({a}^{2} + {b}^{2}\right)}$

taking the square root:

$\left({a}^{2} + {b}^{2}\right) \sqrt{{a}^{2} + {b}^{2}}$

Can we go further than this? No - the addition of the ${a}^{2}$ and ${b}^{2}$ terms means we can't simply take the square root of each piece.