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simplying and factoring

by Greg
(New England)











































7x^3 3/125x^4+3/x^7

the / meant to be square roots

Comments for simplying and factoring

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Jan 12, 2011
Simplifying & Factoring Radical Expressions
by: Staff

The question:
by Greg
(New England)

7x^3 3/125x^4+3/x^7

the / meant to be square roots


The answer:

7x^3 3/125x^4+3/x^7
the / meant to be square roots

------------------------------------------------------------------------------------------

Standard square root terminology - for future reference

any number raised to the ½ power stands for the square root of that number
e.g.: x^(1/2) = the square root of x = sqrt(x)

any number raised to the 1/3 power stands for the cube root of that number
any number raised to the ¼ power stands for the 4th root of that number
and so on …
------------------------------------------------------------------------------------------

7x^3 3/125x^4+3/x^7
the / meant to be square roots

You didn’t indicate what the relationship is (+ or – or *) between the 7x^3 and the 3/125x^4

Since there is a blank space in between, I’m going to assume you meant these two expressions are multiplied

7x^3 3/125x^4+3/x^7
the / meant to be square roots


(7x^3)*3*sqrt(125x^4)+3*sqrt(x^7)

To simplify this expression, begin by factoring the sqrt portions

(7x^3)*3*sqrt(125x^4)+3*sqrt(x^7)

(7x^3)*3*sqrt(5*5*5*x*x*x*x)+3*sqrt(x*x*x*x*x*x*x)

Next, group the values under the square root signs as squares

(7x^3)*3*sqrt(5*5*5*x*x*x*x)+3*sqrt(x*x*x*x*x*x*x)

(7x^3)*3*sqrt[5*(5^2)*(x^2)*x^2)]+3*sqrt[x*(x^2)*(x^2)*(x^2)]

Now split the expressions under the square root signs into separate square roots which are multiplied together

(7x^3)*3*sqrt(5)*sqrt(5^2)*sqrt(x^2)*sqrt(x^2)+3*sqrt(x)*sqrt(x^2)*sqrt(x^2)*sqrt(x^2)

Evaluate the square root where possible

Note: the sqrt(x^2) = x, the sqrt(5^2) = 5


(7x^3)*3*sqrt(5)*sqrt(5^2)*sqrt(x^2)*sqrt(x^2)+3*sqrt(x)*sqrt(x^2)*sqrt(x^2)*sqrt(x^2)


(7x^3)*3*sqrt(5)*5*x*x+3*sqrt(x)*x*x*x

(7x^3)*3*sqrt(5)*5*x*x+3*sqrt(x)*x*x*x

(7x^3)*3*sqrt(5)*5*x^2+3*sqrt(x)* x^3

(7x^3)*3*5*(x^2)*sqrt(5)+3*(x^3)*sqrt(x)

7*(x^3)*(x^2)*15*sqrt(5)+3*(x^3)*sqrt(x)

7*15*(x^3)*(x^2)*sqrt(5)+3*(x^3)*sqrt(x)

105*(x^5)*sqrt(5)+3*(x^3)*sqrt(x)

The final answer: 105*(x^5)*sqrt(5)+3*(x^3)*sqrt(x)


You can’t simplify the expression past this point. However, you can factor out the 3*(x^3) if you wish.

If you factor out the 3*(x^3), the expression will look like this:

[3*(x^3)]*[35*(x^2)*sqrt(5)+ sqrt(x)]




Thanks for writing.


Staff
www.solving-math-problems.com



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