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Square Roots and Simplifying Radicals
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Radical Sign (square root sign)
Radicand Numbers or variables under the radical sign
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Prime Numbers … Perfect Numbers 1, 4, 9, 16, 25, 36, 49…
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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.
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Square numbers have perfect roots!
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Find a perfect number that divides the radicand
EX:1 Find a perfect number that divides the radicand 45= 9*5
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Find a perfect number that divides the radicand
EX:2 Find a perfect number that divides the radicand 98= 49*2
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Find a perfect number that divides the radicand
EX:3 Find a perfect number that divides the radicand 48= 4*12
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Find a perfect number that divides the radicand
EX:4 Find a perfect number that divides the radicand 45= 9*5
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You try!
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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
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15/2 = 7 remainder 1, therefore we leave one variable under the radical
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Multiplying Radicals
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Multiplying Radicals Multiply numbers outside the radical with other numbers outside the radical. Multiply radicands with other radicands. Simplify, if possible
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Example 1 Multiply then simplify if possible.
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Example 2 Distribute then simplify if possible.
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Your Turn
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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!!
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Example 1
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Example 2 Sometimes you have to simplify 1st then see if you can add.
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Simplify
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Simplify
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Simplify
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Simplify
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Simplify
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Simplify
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Simplify
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Simplify
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Simplify
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Simplify
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Simplify
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Simplify
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Simplify
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