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Solving an Equation with Radicals  Problem 1
Carl Horowitz
Carl Horowitz
University of Michigan
Runs his own tutoring company
Carl taught upperlevel math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!
Solving an equation with a square root and a higher root power, so this problem we are looking at a cube root. The steps of solving an equation with a radical are always the same, we want to first get our root by itself take it side your appropriate power to get rid of the root, solve for our variable and then check.
Let’s go through that process right now. First thing we want to do is isolate our root. So we want to get this term cube root of x minus 1 by itself. In order to do that we first need to subtract 3 from both sides we end up with 4 cube root x minus 1 is equal to 8 and then I always like to get the coefficient away as well.
You could move on leaving it there but typically you are just going to get bigger numbers that’s going to make your life a little bit uglier so what we are going to do is divide by 4 to get that root completely by itself.
Our cube root x minus 1 is equal to 2 so now we have the root by itself we want to get rid of the root, we have a cube root so in order to get rid of this root we have to cube it. We cube one side we have to cube the other cube root of cubed just becomes the inside so this is x minus 1 to the third is 8 add 1 is leaves us with 9.
We always want to go back check to make sure our answer works plug in 9, 9 minus 1 is 8 cube root of 8 is 2 4 times 2 is 8 plus 3 is 11.
So this answer actually checks out so by going through the steps of solving a quadratic equation we are able to solve this problem.
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Carl Horowitz
B.S. in Mathematics University of Michigan
He knows how to make difficult math concepts easy for everyone to understand. He speaks at a steady pace and his stepbystep explanations are easy to follow.
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Sample Problems (13)
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Solving an Equation with Radicals
Problem 1 5,085 viewsSolve:
4 ⋅ ∛x − 1 + 3 = 11 
Solving an Equation with Radicals
Problem 2 4,636 viewsSolve:
√x + 2 = x 
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Problem 3 4,338 viewsSolve:
√3x − 2 − √x + 3 = 1 
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Problem 4 629 views 
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Problem 5 549 views 
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Problem 6 525 views 
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Problem 8 561 views 
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Problem 9 601 views 
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Problem 10 556 views 
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Problem 11 571 views 
Solving an Equation with Radicals
Problem 12 502 views 
Solving an Equation with Radicals
Problem 13 547 views
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