I have a quick question on square roots.

[DTRapture]

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 x^3/5 because, eh, who knows.

 

[jedishrfu]

The 5 is just a factor like sort(50) = 5*sqrt(2)

In your case it is 5 * sqrt(x^3)

 

[DTRapture]

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.

 

[jedishrfu]

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?

 

[DTRapture]

I'll assume that it's x^3/5?

 

[jedishrfu]

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?

 

[DTRapture]

Then yeah, it is x^3/5.

Like how the 7th root of y and y=x³ will be x^3/7

 

[jedishrfu]

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...

 

[Mark44]

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: $x^{3/5}$

 

[mathman]

To clarify the notation \sqrt {} mean square root when there is no number. \sqrt[n] {} means nth root.