SOLUTION: I am trying to help my son with his algebra and I have run into a problem that I can't figure out. The problem is as follows:
Multiply and then simplify by factoring
√x
Algebra.Com
Question 488552: I am trying to help my son with his algebra and I have run into a problem that I can't figure out. The problem is as follows:
Multiply and then simplify by factoring
√x √2x √10x^5
(just in case they don't appear correctly they are: sqrt x sqrt 2x sqrt 10x^5)
If someone could please explain the steps, I would appreciate it and it would keep me from having to post again :)
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
you are looking at:
sqrt(x) * sqrt(2x) * sqrt(10x^5) i believe.
you want to multiply these all together if i understand you correctly in order to simplify the expression.
in general, sqrt(a) times sqrt(b) equals sqrt(a * b)
that means that:
sqrt(x) * sqrt(2x) * sqrt(10x^5) = sqrt(x * 2x * 10x^5) which becomes:
sqrt(20x^7)
this is because x * 2 * x * 10 * x^5 is equivalent to:
x * x * x^5 * 2 * 10 which is equivalent to:
x^2 * x^5 * 20 which is equivalent to:
x^7 * 20 which is equivalent to:
20 * x^7 which can be shown as:
20x^7
the ability to make x * x * 2 * x = 2 * x * x * x is the law of commutativity.
this law says that a * b is the same as b * a
the ability to make x * x = x^2 is the algebraic law of exponents that says that a^b * a^c is equal to a^(b + c)
you need to simplify this and you should be done.
sqrt(20x^7) is equal to sqrt(4*5*x^2*x^2*x^2*x)
you can bring out the 4 from under the square root sign because the square root of 4 is 2.
the expression becomes 2 * sqrt(5*x^2*x^2*x^2*x)
you can bring out 3 of the x^2 terms from under the square root sing because the square root of x^2 is equal to x.
the expression becomes 2 * x * x * x * sqrt(5x)
since x * x * x = x^3, then your expression becomes:
2 * x^3 * sqrt(x)
that should be as simplified as it gets.
the final expression is 2x^3sqrt(x) which looks like this:
if you want to show that the final expression is equivalent to the original expression, then just pick a random value for x and solve both the original expression and the final expression.
if they give you the same answer then you did good.
the original expression is:
sqrt(x) * sqrt(2x) * sqrt(10x^5)
the final expression is:
2 * x^3 * sqrt(x)
we'll pick a random value for x of 7 and use the calculator to solve the original expression and the final expression.l
the original expression becomes 4058.430731
the final expression becomes 4058.430731
i get the same answer so the simplification was done correctly.
here's a couple of references that might help you to understand this better.
http://www.bymath.com/studyguide/ari/ari4.html
http://www.mathsisfun.com/algebra/exponent-laws.html
http://www.school-for-champions.com/algebra/properties_add_multiply.htm
http://www.wtamu.edu/academic/anns/mps/math/mathlab/int_algebra/int_alg_tut39_simrad.htm
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