Integrated Math 2 / Unit 1: Exponents and Radicals
1.5 Operations with Radicals
Notes
Radicals combine like algebra terms.
- Add or subtract only like radicals (same radicand): $\displaystyle 3\sqrt{5} + 4\sqrt{5} = 7\sqrt{5}$.
- Simplify first, since unlike radicals may become like: $\displaystyle \sqrt{12} + \sqrt{27} = 2\sqrt{3} + 3\sqrt{3} = 5\sqrt{3}$.
- Multiply radicands: $\displaystyle \sqrt{6} \cdot \sqrt{10} = \sqrt{60} = 2\sqrt{15}$.
- Rationalize a denominator by multiplying top and bottom by the radical: $\displaystyle \frac{6}{\sqrt{3}} = \frac{6\sqrt{3}}{3} = 2\sqrt{3}$.
Practice
Simplify $\displaystyle 3\sqrt{5} + 4\sqrt{5}$.
Like radicals add their coefficients and the radical stays the same.
Simplify $\displaystyle \sqrt{12} + \sqrt{27}$.
$\displaystyle \sqrt{12} = 2\sqrt{3}$ and $\displaystyle \sqrt{27} = 3\sqrt{3}$, so the sum is $\displaystyle 5\sqrt{3}$.
Rationalize the denominator: $\displaystyle \frac{6}{\sqrt{3}}$.
Multiply top and bottom by $\displaystyle \sqrt{3}$ to get $\displaystyle \frac{6\sqrt{3}}{3} = 2\sqrt{3}$.
Ready for more? Take the Unit 1 test.