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Square Roots

Opposite of applying exponents.

$\sqrt{\ }\ \Rightarrow\ square\ root,\ \sqrt[3]{\ }\ \Rightarrow\ cube\ root$

To simplify square roots take out perfect squares.

$\sqrt{4}=\sqrt{2^2}=2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \sqrt{12}=\sqrt{4\times3}=\sqrt{2^{2}\times 3}=2\sqrt{3}$

Simplifying complex expressions:

Rewrite grouping perfect squares
- $\sqrt{2^{2}5x^{2}x^{2}xy^{2}y^{2}y^{2}yz^{2}$
Pull out perfect squares
- $2x^{2}y^{3}z\sqrt{5xy}$

Simplifying cube roots by pulling out perfect cubes:

Use of square roots in pythagorean theorem:

$a^{2}+b^{2}=c^{2}$

$a=5,\ b=12$

$5^{2}+12^{2}=c^{2}$

$160=c^{2}$

* take square root to undo exponent

$\sqrt{169}=\sqrt{c^2}$

$13=c$