Square Roots and Simplifying Radicals

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Presentation transcript:

Square Roots and Simplifying Radicals

Radical Sign (square root sign) Radicand Numbers or variables under the radical sign

Prime Numbers 2 3 5 7 11 13… Perfect Numbers 1, 4, 9, 16, 25, 36, 49…

Radicals are in SIMPLEST FORM when.. 1. No perfect square factors other than 1 are under the radical. No fractions are under the radical. No radicals are in the denominator.

Square numbers have perfect roots!

Find a perfect number that divides the radicand EX:1 Find a perfect number that divides the radicand 45= 9*5

Find a perfect number that divides the radicand EX:2 Find a perfect number that divides the radicand 98= 49*2

Find a perfect number that divides the radicand EX:3 Find a perfect number that divides the radicand 48= 4*12

Find a perfect number that divides the radicand EX:4 Find a perfect number that divides the radicand 45= 9*5

You try! 1. 2. 3. 4.

Variables as Radicands Even Exponent – ODD Exponent – Take HALF out (nothing left under the radical) Leave ONE under the radical and take HALF of the rest out

15/2 = 7 remainder 1, therefore we leave one variable under the radical

Multiplying Radicals

Multiplying Radicals Multiply numbers outside the radical with other numbers outside the radical. Multiply radicands with other radicands. Simplify, if possible

Example 1 Multiply then simplify if possible.

Example 2 Distribute then simplify if possible.

Your Turn

Add and Subtract Radicals You can only add or subtract radicals that have the EXACT SAME radicand. Then add/subtract ONLY the number OUTSIDE the radical Then, check to see if you can simplify!!

Example 1

Example 2 Sometimes you have to simplify 1st then see if you can add.

Simplify

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Simplify