Lesson Simplify Radicals

This Lesson (Simplify Radicals) was created by by Shruti_Mishra(0)

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About Shruti_Mishra: I am a maths graduate from India and am currently persuing masters in Operations Research.

Using the properties of radicals, we would learn how to simplify radicals. We would use examples to learn how to simplify the expressions and then generalize.

Simplification with radical of a multiple
Q. root%283%2C40%29

Solution.

Solution.

Thus we see that we can bring the factors with powers equal to the root of the radical. Thus if we have root%28n%2Cx%29

where

where m,k>n and l

Simplification of additions
Q. 5%2Aroot%283%2C7%29%2B+3%2Aroot%283%2C7%29

Solution:

Solution:

Thus we see that the expressions with same radicals can be added directly as: a%2Aroot%28n%2Cx%29%2Bb%2Aroot%28n%2Cx%29+=+%28a%2Bb%29%2Aroot%28n%2Cx%29

Product of radicals
Q. Write root%283%2C15%29

as a product of two radicals
Solution: root%283%2C15%29+=+root%283%2C3%2A5%29+=+root%283%2C3%29%2Aroot%283%2C5%29

Q. Simplify sqrt%285%29%2Asqrt%2810%29%2Asqrt%282%29

Solution:

Thus we can split the radical by factorizing the number in the radical. Also, we can simplify radicals by multiplying them and combining the powers to bring some factors out of the radical sign.

Multiplying radical expressions
Q. Simplify %28sqrt%283%29%2Bsqrt%282%29%29%2A%28sqrt%286%29%2Bsqrt%285%29%29

Solution: Opening the parentheses, we get
%28sqrt%283%29%2Bsqrt%282%29%29%2A%28sqrt%286%29%2Bsqrt%285%29%29

sqrt%283%2A3%2A2%29+%2B+sqrt%282%2A2%2A3%29+%2B+sqrt%283%2A5%29+%2B+sqrt%282%2A5%29

3%2Asqrt%282%29%2B2%2Asqrt%283%29%2Bsqrt%2815%29%2Bsqrt%2810%29

Q. Simplify %28sqrt%283%29%2Bsqrt%282%29%29%2A%28sqrt%283%29-sqrt%282%29%29

Solution: We know %28sqrt%28a%29%2Bsqrt%28b%29%29%2A%28sqrt%28a%29-sqrt%28b%29%29+=+a-b

Thus

%28sqrt%283%29%2Bsqrt%282%29%29%2A%28sqrt%283%29-sqrt%282%29%29+=+3-2+=1

Thus we see we can multiply the radicals by simplifying the parentheses and then simplifying the radical expressions.

Radicals in denominator
Q. Simplify 5%2Fsqrt%283%29

Solution:

Q. Simplify 2%2F%28sqrt%283%29-sqrt%281%29%29

Solution:

Thus we try to remove the radicals from the denominator using the properties of radicals.

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