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Simplifying radicals

\sqrt{20m {}^(4) } n {}^(3)


User Tushant
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1 Answer

6 votes

Answer: 2m^2n.\sqrt{5}

Step-by-step explanation: Factor 20 into its prime factors

20 = 22 • 5

To simplify a square root, we extract factors which are squares, i.e., factors that are raised to an even exponent.

Factors which will be extracted are :

4 = 22

Factors which will remain inside the root are :

5 = 5

To complete this part of the simplification we take the squre root of the factors which are to be extracted. We do this by dividing their exponents by 2 :

2 = 2

At the end of this step the partly simplified SQRT looks like this:

2 • sqrt (5m4n3)

Rules for simplifing variables which may be raised to a power:

(1) variables with no exponent stay inside the radical

(2) variables raised to power 1 or (-1) stay inside the radical

(3) variables raised to an even exponent: Half the exponent taken out, nothing remains inside the radical. examples:

(3.1) sqrt(x8)=x4

(3.2) sqrt(x-6)=x-3

(4) variables raised to an odd exponent which is >2 or <(-2) , examples:

(4.1) sqrt(x5)=x2•sqrt(x)

(4.2) sqrt(x-7)=x-3•sqrt(x-1)

Applying these rules to our case we find out that

SQRT(m4n3) = m2n • SQRT(n)

sqrt (20m4n3) =

2 m2n • sqrt(5n)

2 m2n • sqrt(5n)

User Sarunast
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