Absolute Value Equations
\pi \cdot \pi
Absolute Value Equations
What is an Absolute Value?
- The positive value of a number.
- The positive value of a number.
Division of Radicals
Division of Radicals
Ex 1: Simplify \(\frac{15 \sqrt[3]{108}}{20 \sqrt[3]{2}}\)
\(\frac{15 \sqrt[3]{108}}{20 \sqrt[3]{2}}\)
=\(\frac{15}{20} \cdot \sqrt[3]{\frac{108}{2}}\)
=\(\frac{15}{20} \cdot \sqrt[3]{54}\)
=\(\frac{15}{20} \cdot \sqrt[3]{27 \cdot 2}\)
=\(\frac{15}{20} \cdot \sqrt[3]{27} \cdot \sqrt[3]{2}\)
=\(\frac{15}{20} \cdot 3 \cdot \sqrt[3]{2}\)
=\(\frac{\cancel{15}^{~3}}{\cancel{20}^{~4}} \cdot 3 \cdot \sqrt[3]{2}\)
=\(\frac{9\sqrt[3]{2}}{4}\)
Division of Radicals
Division of Radicals
Ex 1: Simplify \(\frac{15 \sqrt[3]{108}}{20 \sqrt[3]{2}}\)
\(\frac{15 \sqrt[3]{108}}{20 \sqrt[3]{2}}\)
=\(\frac{15}{20} \cdot \sqrt[3]{\frac{108}{2}}\)
=\(\frac{15}{20} \cdot \sqrt[3]{54}\)
=\(\frac{15}{20} \cdot \sqrt[3]{27 \cdot 2}\)
=\(\frac{15}{20} \cdot \sqrt[3]{27} \cdot \sqrt[3]{2}\)
=\(\frac{15}{20} \cdot 3 \cdot \sqrt[3]{2}\)
=\(\frac{\cancel{15}^{~3}}{\cancel{20}^{~4}} \cdot 3 \cdot \sqrt[3]{2}\)
=\(\frac{9\sqrt[3]{2}}{4}\)
Division of Radicals
Division of Radicals
Ex 1: Simplify \(\frac{15 \sqrt[3]{108}}{20 \sqrt[3]{2}}\)
\(\frac{15 \sqrt[3]{108}}{20 \sqrt[3]{2}}\)
=\(\frac{15}{20} \cdot \sqrt[3]{\frac{108}{2}}\)
=\(\frac{15}{20} \cdot \sqrt[3]{54}\)
=\(\frac{15}{20} \cdot \sqrt[3]{27 \cdot 2}\)
=\(\frac{15}{20} \cdot \sqrt[3]{27} \cdot \sqrt[3]{2}\)
=\(\frac{15}{20} \cdot 3 \cdot \sqrt[3]{2}\)
=\(\frac{\cancel{15}^{~3}}{\cancel{20}^{~4}} \cdot 3 \cdot \sqrt[3]{2}\)
=\(\frac{9\sqrt[3]{2}}{4}\)
Division of Radicals
Division of Radicals
Ex 1: Simplify \(\frac{15 \sqrt[3]{108}}{20 \sqrt[3]{2}}\)
\(\frac{15 \sqrt[3]{108}}{20 \sqrt[3]{2}}\)
=\(\frac{15}{20} \cdot \sqrt[3]{\frac{108}{2}}\)
=\(\frac{15}{20} \cdot \sqrt[3]{54}\)
=\(\frac{15}{20} \cdot \sqrt[3]{27 \cdot 2}\)
=\(\frac{15}{20} \cdot \sqrt[3]{27} \cdot \sqrt[3]{2}\)
=\(\frac{15}{20} \cdot 3 \cdot \sqrt[3]{2}\)
=\(\frac{\cancel{15}^{~3}}{\cancel{20}^{~4}} \cdot 3 \cdot \sqrt[3]{2}\)
=\(\frac{9\sqrt[3]{2}}{4}\)
Division of Radicals
Division of Radicals
Ex 1: Simplify \(\frac{15 \sqrt[3]{108}}{20 \sqrt[3]{2}}\)
\(\frac{15 \sqrt[3]{108}}{20 \sqrt[3]{2}}\)
=\(\frac{15}{20} \cdot \sqrt[3]{\frac{108}{2}}\)
=\(\frac{15}{20} \cdot \sqrt[3]{54}\)
=\(\frac{15}{20} \cdot \sqrt[3]{27 \cdot 2}\)
=\(\frac{15}{20} \cdot \sqrt[3]{27} \cdot \sqrt[3]{2}\)
=\(\frac{15}{20} \cdot 3 \cdot \sqrt[3]{2}\)
=\(\frac{\cancel{15}^{~3}}{\cancel{20}^{~4}} \cdot 3 \cdot \sqrt[3]{2}\)
=\(\frac{9\sqrt[3]{2}}{4}\)
Division of Radicals
Division of Radicals
Ex 1: Simplify \(\frac{15 \sqrt[3]{108}}{20 \sqrt[3]{2}}\)
\(\frac{15 \sqrt[3]{108}}{20 \sqrt[3]{2}}\)
=\(\frac{15}{20} \cdot \sqrt[3]{\frac{108}{2}}\)
=\(\frac{15}{20} \cdot \sqrt[3]{54}\)
=\(\frac{15}{20} \cdot \sqrt[3]{27 \cdot 2}\)
=\(\frac{15}{20} \cdot \sqrt[3]{27} \cdot \sqrt[3]{2}\)
=\(\frac{15}{20} \cdot 3 \cdot \sqrt[3]{2}\)
=\(\frac{\cancel{15}^{~3}}{\cancel{20}^{~4}} \cdot 3 \cdot \sqrt[3]{2}\)
=\(\frac{9\sqrt[3]{2}}{4}\)
Division of Radicals
Division of Radicals
Ex 1: Simplify \(\frac{15 \sqrt[3]{108}}{20 \sqrt[3]{2}}\)
\(\frac{15 \sqrt[3]{108}}{20 \sqrt[3]{2}}\)
=\(\frac{15}{20} \cdot \sqrt[3]{\frac{108}{2}}\)
=\(\frac{15}{20} \cdot \sqrt[3]{54}\)
=\(\frac{15}{20} \cdot \sqrt[3]{27 \cdot 2}\)
=\(\frac{15}{20} \cdot \sqrt[3]{27} \cdot \sqrt[3]{2}\)
=\(\frac{15}{20} \cdot 3 \cdot \sqrt[3]{2}\)
=\(\frac{\cancel{15}^{~3}}{\cancel{20}^{~4}} \cdot 3 \cdot \sqrt[3]{2}\)
=\(\frac{9\sqrt[3]{2}}{4}\)
Division of Radicals
Division of Radicals
Ex 1: Simplify \(\frac{15 \sqrt[3]{108}}{20 \sqrt[3]{2}}\)
\(\frac{15 \sqrt[3]{108}}{20 \sqrt[3]{2}}\)
=\(\frac{15}{20} \cdot \sqrt[3]{\frac{108}{2}}\)
=\(\frac{15}{20} \cdot \sqrt[3]{54}\)
=\(\frac{15}{20} \cdot \sqrt[3]{27 \cdot 2}\)
=\(\frac{15}{20} \cdot \sqrt[3]{27} \cdot \sqrt[3]{2}\)
=\(\frac{15}{20} \cdot 3 \cdot \sqrt[3]{2}\)
=\(\frac{\cancel{15}^{~3}}{\cancel{20}^{~4}} \cdot 3 \cdot \sqrt[3]{2}\)
=\(\frac{9\sqrt[3]{2}}{4}\)
Division of Radicals
Division of Radicals
Ex 2: Simplify \(\frac{\sqrt{6}}{\sqrt{5}}\)
\(\frac{\sqrt{6}}{\sqrt{5}}\)
=\(\frac{\sqrt{6}}{\sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}}\)
=\(\frac{\sqrt{6} \cdot \sqrt{5}}{\sqrt{5} \cdot \sqrt{5}}\)
=\(\frac{\sqrt{6 \cdot 5}}{5}\)
=\(\frac{\sqrt{30}}{5}\)
Division of Radicals
Division of Radicals
Ex 3: Simplify \(\frac{\sqrt{6}}{\sqrt{5}}\)
\(\frac{\sqrt{6}}{\sqrt{5}}\)
=\(\frac{\sqrt{6}}{\sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}}\)
=\(\frac{\sqrt{6} \cdot \sqrt{5}}{\sqrt{5} \cdot \sqrt{5}}\)
=\(\frac{\sqrt{6 \cdot 5}}{5}\)
=\(\frac{\sqrt{30}}{5}\)
\pi \cdot \pi
Absolute Value Equations
By Anurag Katyal
