I have a quick question on square roots.

In summary, the conversation discusses how to simplify an expression with a fifth root and a variable raised to a power. The answer is x^(3/5) and the conversation also mentions the importance of understanding patterns in calculus.
  • #1
DTRapture
5
0
There's this problem on my homework that says something like 5√x3, except the 5 is like an exponent directly to the left of the square root sign. I'm not sure how to solve it, but I'm just guessing that the answer is x3/5 because, eh, who knows.
 
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  • #2
The 5 is just a factor like sort(50) = 5*sqrt(2)

In your case it is 5 * sqrt(x^3)
 
  • #3
ImageUploadedByPhysics Forums1439704716.244603.jpg


I'm confused. The problem looks like this, labeled next to the "7". I don't know the steps to simplify/solve it.

I looked at the answer key and the answer actually was x^3/5, but I don't know how to get that answer.
 
  • #4
Okay that's different from what you typed. It means the 5th root not the square root. so yes it can be written as x^(3/5) or in english as x to the three fifths power.

So a square root is x^(1/2) and a cube root is x^(1/3) so a fifth root is x^(1/5) Do you see the pattern?

Since the number under the root is x^3 then what is the answer?
 
  • #5
I'll assume that it's x3/5?
 
  • #6
Don't assume. You need to know the answer

if its the 5th root of y and y=x^3 then what's the answer?
 
  • #7
Then yeah, it is x3/5.

Like how the 7th root of y and y=x3 will be x3/7
 
  • #8
Yes, I think you have it.

A lot of Calculus will depend on your ability to see these patterns and to understand how you can substitute expressions into variables...
 
  • #9
DTRapture said:
View attachment 87377

I'm confused. The problem looks like this, labeled next to the "7". I don't know the steps to simplify/solve it.

I looked at the answer key and the answer actually was x^3/5, but I don't know how to get that answer.
It would be helpful if you had written the entire problem statement. According to what you showed as the answer you are neither simplifying nor solving the problem. All that you are supposed to do is rewrite the radical expression in exponent notation.
Radical notation: ##\sqrt[5]{x^3}##
Exponent notation: ##x^{3/5}##
 
  • #10
To clarify the notation [itex] \sqrt {} [/itex] mean square root when there is no number. [itex]\sqrt[n] {}[/itex] means nth root.
 

Related to I have a quick question on square roots.

1. What is a square root?

A square root is the number that, when multiplied by itself, gives the original number. For example, the square root of 25 is 5 because 5 multiplied by itself equals 25.

2. How do I find the square root of a number?

There are a few different methods for finding square roots, including using a calculator, using long division, or using estimation techniques. It depends on the complexity of the number and the level of accuracy needed.

3. Can a negative number have a square root?

Yes, negative numbers can have square roots. However, they are considered imaginary numbers and cannot be represented on a number line. Instead, they are denoted with the letter "i" and are used in complex numbers.

4. What is the difference between a square root and an exponent?

A square root is the inverse operation of squaring a number. It is represented by the symbol √ and takes a number and finds the value that, when squared, equals the original number. An exponent, on the other hand, is a number that indicates how many times a base number should be multiplied by itself. For example, 2³ means 2 multiplied by itself 3 times.

5. Why are square roots important?

Square roots are important in many real-world applications, such as calculating the area of a square or finding the length of the sides of a right triangle. They are also used in advanced mathematical concepts like calculus and physics.

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