Lesson Properties and Operations of Radicals

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This Lesson (Properties and Operations of Radicals) was created by by Shruti_Mishra(0) About Me : View Source, Show
About Shruti_Mishra: I am a maths graduate from India and am currently persuing masters in Operations Research.
The properties of radicals help in solving and simplifying radicals.

Adding two radicals (simplest form)
For adding two radicals, the number under the radical sign should be same in the two radicals (in the simplest form). The operation is:
a%2Aroot%28n%2Cx%29+%2B+b%2Aroot%28n%2Cx%29+=+%28a%2Bb%29%2Aroot%28n%2Cx%29


Subtracting two radicals (simplest form)
For subtracting two radicals, the number under the radical sign should be same in the two radicals (in the simplest form). The operation is:
a%2Aroot%28n%2Cx%29+-+b%2Aroot%28n%2Cx%29+=+%28a-b%29%2Aroot%28n%2Cx%29


Operations on radicals with same 'n'

root%28n%2Cx%2Ay%29+=+root%28n%2Cx%29%2Aroot%28n%2Cy%29
root%28n%2Cx%2Fy%29+=+root%28n%2Cx%29%2Froot%28n%2Cy%29
root%28n%2Cx%2Ay%2Az%29+=+root%28n%2Cx%29%2Aroot%28n%2Cy%29%2Aroot%28n%2Cz%29


Operations on radicals with different 'n'







Other Operations
1. If m > n in root%28n%2Cx%5Em%29, then
2. sqrt%28x%5E2%2Ay%29=x%2Asqrt%28y%29
3. root%28n%2Cx%5Em%2Ay%29=x%5E%28m%2Fn%29%2Aroot%28n%2Cy%29
4.
5.
6. x%2Fsqrt%28y%29=+x%2Asqrt%28y%29%2Fsqrt%28y%29%5E2+=+x%2Asqrt%28y%29%2Fy
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