Week 3: Radical

Published by on February 19, 2018 | Leave a response

In radical, there are some basic knowledge:
a\sqrt[i]{b}
where:
a: coefficient
b: radicand (b\geq 0 if i is an even number)
i: index
* Simplify radicals
– Square root: (Divide the radicand by the perfect square starting from the smallest number to create factors from the radicand.)
Example:
\sqrt{81}
=\sqrt{9.9}
=\sqrt{9}.\sqrt{9}
=3.3
=9
\sqrt{384}
=\sqrt{4.4.4.6}
=\sqrt{4}.\sqrt{4}.\sqrt{4}.\sqrt{6}
=2.2.2\sqrt{6}
=8\sqrt{6}
\sqrt{\frac{12}{45}}
=\sqrt{\frac{4}{9}.\frac{3}{5}}
=\frac{2}{3}.\sqrt{\frac{3}{5}}
\sqrt{54.x^3} (Restriction:x\geq 0)
=\sqrt{9.6.x^2.x}
=3x.\sqrt{6x}
– Other roots:
Example:
\sqrt[3]{\frac{-32.x^4}{81}}
=\sqrt[3]{\frac{-8.4.x^3.x}{27.3}}
=\frac{-2x}{3}.\sqrt[3]{\frac{4x}{3}} or \frac{2x}{3}.\sqrt[3]{\frac{-4x}{3}}
* Entire radical
– Square root: (Square the coefficient and put it in a square root at the same time)
Example:
-4\sqrt{6}
=-\sqrt{4^2.6}
=-\sqrt{16.6}
=-\sqrt{96}
– Other roots:
Example:
\frac{-2x}{3}.\sqrt[3]{\frac{3}{4}}
=\sqrt[3]{\frac{-2^3.x^3}{3^3}.\frac{3}{4}}
=\sqrt[3]{\frac{-8.x^3}{27}.\frac{3}{4}}
=\sqrt[3]{\frac{-27.x^3}{108}}

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