Radicals
By DarthVader
Date: 2021-10-20
Topic: 68 see comments
Post views: 1271
Radicals
Addition:
Example 1: √3 + 3 = √6
Example 2: -√2 -√2 = -2√2
Example 3: 3√3 + 4√3 = 7√3
You can only add/subtract like radicals (radicals with the same value under the radical sign)
E.G.
4√3 + 5√3 = 9√3
So when adding a bunch of radicals, the first thing to do is simplify each term, then add the coefficients and the like terms
Multiplication:
Rules: √a × √b = √a × b
To multiply radicals, multiply whats under the radical sign
E.G.
√7 × √7 = √7 × 7
√7 × 7 = √49
√49 = 7
E.G.
Multiply the coefficient seperately:
(4√3)(2√2) = 8√6
Division:
- Extend the radical sign and simplify: √12x3 / √27x = √4
12x32 / 927x= √4x2 / 9 - Put the numerator and denominator back under radical signs: = √4x2 / √9
- Simplify each radical: √4x2 / √9 = 2x / 3
Radicals are not allowed as the denominator of a fraction
You must multiply the fraction by the conjugate, to get rid of the radical on the bottom:
E.G.
6 / 7 + 7√2 = 6(7 - 7√2) / (7 + 7√2)(7 – 7√2)
Here the Conjugate is: 7 − 7√2
ALWAYS SIMPLIFY YOUR ANSWER
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