LaTeX is your friend. See the link to our tutorial in the lower left corner of the input window.EvilScientist said:Summary: Finding the root to an exponent that's larger than the root.
I feel incredibly stupid for not getting this. I found this math problem in the beginning of my precalculus book:
12√x^4
That's 12th root of x to the fourth power. How do I find the root of x if the root is larger than the exponent?
Thank you! It makes a lot more sense to me now. I haven't done this stuff in years and I am trying to brush off my math skills before taking any classes. Needless to say, my math skills are very rusty. Thanks again, I really appreciate it. I'll try learning how to use LaTeX, I'm probably going to need it later.Mark44 said:LaTeX is your friend. See the link to our tutorial in the lower left corner of the input window.
##\sqrt[12]{x^4}## can be rewritten as ##(x^4)^{1/12} = x^{4/12} = x^{1/3}## using the usual laws of exponents. A simpler form of your expression is ##\sqrt[3] x##.
And technically, this is not something to "solve," an action that we can apply to equations or inequalities. What I did was to simplify the expression you wrote.
Start now! Its like riding a bicycle...maybe less fun to learn.EvilScientist said:I'll try learning how to use LaTeX
This has nothing to do with calculus -- ##\sqrt[12]{25^{4}} = \sqrt[3]{25}## is the exact value, but this happens to be irrational, so writing it as a decimal number will be only an approximation. BTW, ##\sqrt[3]{25}## is little less than 3.mcastillo356 said:Hi, @EvilScientist , could your question hide a deeper concern? Calculus. I mean, nobody knows the value of ##\sqrt[12]{x^{4}}##, if ##x=25##, for instance. Only knows can approximate.
Finding the root of x^4 means finding the value of x that, when raised to the fourth power, equals a given number. This is also known as solving for x in the equation x^4 = y, where y is a given number.
To find the root of x^4, you can use the inverse operation of raising a number to the fourth power, which is taking the fourth root. This can be done by using a calculator or by using the power rule for radicals, where the fourth root of x^4 is equal to the square root of the square root of x.
Yes, the root of x^4 can be a negative number. This is because when a negative number is raised to an even power, the result is a positive number. For example, the fourth root of (-2)^4 is equal to 2.
The root of x^4 is the value of x that, when raised to the fourth power, equals a given number. The fourth root of x, on the other hand, is the number that, when raised to the fourth power, equals x. In other words, the root of x^4 is the solution to the equation x^4 = y, while the fourth root of x is the inverse operation of raising x to the fourth power.
Yes, the root of x^4 can be a complex number. This can happen when the given number y is a negative number, as the fourth root of a negative number is a complex number. For example, the fourth root of -16 is equal to 2i, where i is the imaginary unit.