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Removing the multiplier from under the root sign and adding it under the root sign

If a=b2ca=b^2c with b≥0, c≥0b\ge0,\ c\ge0, then a=bc\sqrt{a}=b\sqrt{c} — we have factored bb out of the radical. The reverse move: ka=k2ak\sqrt{a}=\sqrt{k^2a} for k≥0k\ge0 — moving a factor under the radical sign.
First split the radicand into factors, one of which is a perfect square
When moving a factor in, remember to square it under the radical
The answer is often written with a square-free part under the radical
Factor out of the radical.
Simplify the radical
50\sqrt{50}
=52=5\sqrt{2}
50=25⋅2\sqrt{50}=\sqrt{25\cdot2}=52=5\sqrt{2}
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