Learn how to rewrite square roots (and expressions containing them) so there's no perfect square within the square root. For example, rewrite √75 as 5⋅√3.

Worked examples of taking expressions with square roots and taking all of the perfect squares out of the square roots. For example, 2√ (7x)⋅3√ (14x²) can be written as 42x√ (2x).

When I look at Simplifying Square Roots, it reminds me a lot of Prime factorization. In fact, I have been following along with these videos on Simplifying Square Roots, using the same method …

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Simplify. Remove all perfect squares from inside the square root. Assume b is positive.

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What about roots that aren't equal to an integer, like √20? Still, we can write 20 as 4⋅5 and then use known properties to write √ (4⋅5) as √4⋅√5, which is 2√5.

Any variable that can be squared so for instance x^2 or y^4 is taken out of the square root symbol. You then divide the exponent by 2 (so x^2 would be x^1 or just x and y^4 would be y^2). Once …

Simplify. Remove all perfect squares from inside the square root. Assume b is positive.