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**Prove It** I always look for square factors. It doesn't matter what the square factor is, because you can always simplify further later if needbe.

$\displaystyle \sqrt{180} = \sqrt{18\cdot 10}$

$\displaystyle = \sqrt{2\cdot 9 \cdot 2 \cdot 5}$

$\displaystyle = \sqrt{2^2\cdot 3^2 \cdot 5}$

$\displaystyle = \sqrt{2^2\cdot 3^2}\sqrt{5}$

$\displaystyle = 2\cdot 3 \sqrt{5}$

$\displaystyle = 6\sqrt{5}$.

For the second

$\displaystyle \sqrt{2197} = \sqrt{13^3}$

$\displaystyle = \sqrt{13^2}\sqrt{13}$

$\displaystyle = 13\sqrt{13}$.