Radicals Simplify, Add, Subtract, Multiply, Divide and Rationalize

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Presentation transcript:

Radicals Simplify, Add, Subtract, Multiply, Divide and Rationalize

What is a radical? It is a symbol placed over a number to indicate the root of a number.

Radicals square root cube root fourth root nth root Radical symbol Index of the radical Radical symbol radicand

Here are examples of radicals seen before What type of numbers are 25, 36,49 and 100?

Perfect Squares 02 = 0 12 = 1 22 = 4 32 = 9 42 = 16 52 = 25 62 = 36 72 = 49 82 = 64 92 = 81 102 = 100 112 = 121 122 = 144 132 = 169 142 = 196 152 = 225 162 = 256 172 = 289 182 = 324 192 = 361 202 = 400 212 = 441 222 = 484 232 = 529 242 = 576 252 = 625 262 = 676 272 = 729 282 = 784 292 = 841 302 = 900 …..

Simplest Form A radical expression is in simplest form if the following conditions are true: No perfect square factors are in the radicand No fractions are in the radicand No radicals appear in the denominator of a fraction

**Simplifying Radicals** Find the square root of each number by using the factors (prime factorization!) 81 147 9 9 3 49 Circle the pairs 3 3 3 3 7 7 One number from each pair goes on the outside of the radical (multiplied). All else stays on the inside. = 3 • 3 = 9

**Simplifying Radicals** Find the square root of each number by using the factors 360 52 525 36 10 2 26 15 35 6 6 2 5 2 13 3 5 5 7 3 3 2 2

Multiplying and Dividing Radicals **Multiplying and Dividing Radicals** Multiply “outside the radical times outside the radical” times “inside the radical times inside the radical”. Same thing with dividing but change the word multiply to divide.

Adding and Subtracting Radicals. THEY MUST HAVE THE SAME RADICAL **Adding and Subtracting Radicals** THEY MUST HAVE THE SAME RADICAL!!!! Sometimes you will have to simplify the radicals first! Simplify root 8 1st.

Rationalizing the Denominator. NO RADICALS IN THE DENOMINATOR **Rationalizing the Denominator** NO RADICALS IN THE DENOMINATOR!!!! Instead, multiply the numerator and denominator by the radical in the bottom: