1. ### Radicals and absolute value

Hey. We all know that sqrt (x^2) = |x|. But what about sqrt(x^4), x^(2/4) and so.. are we required to use absolute values here? And why?
2. ### Proving certain radicals are irrational

Prove \sqrt{2} + \sqrt{3} is an irrational number. My attempt to solve this problem is to equate \sqrt{2} + \sqrt{3} to \frac{a}{b} and show that a or b cannot be integers. I don't know how to do that.

could someone explain this to me or send me to a video that would explain it? thanks
4. ### An issue I've noticed with algebra lately

Lately, I've been noticing a lot of contradictions, between two or more rules in algebra. One that comes to mind is the fact that radicals are considered to be a type of grouping symbol, but then the lesson tells you to simplify a radical expression and (indirectly) disregard the previously...

Need help ! Thank you very much !

Can someone help explain how to simplify this problem? (3xy^1/2)(4x^2y)^-2 ___________________ xy^3/2 note: the answer is xy^2
7. ### Why does the order of these radicals matter?

I'm reviewing slews of math for an upcoming college placement exam, and there's a practice question that demands I rationalize the denominator. The statement is thus: Rationalize the denominator. 7 divided by (square root of 6 plus square root of 13) \frac {7}{\sqrt{6} + \sqrt{13}} I guessed...

Hello everyone, So, I encountered a very strange trend that I am having trouble understanding. I am given f(x)= âˆš(x-2) and g(x)=âˆš(x+5) and am told to find f(g). g(f), f(f), g(g). In f(g), âˆš(âˆš(x+5) - 2), after setting the equation to zero, squaring both sides, I get x=-1 and the...

Hello! How do \sqrt{4}?
10. ### Evaluating expression with Radicals

Hello, I believe I've completed a problem but I'm not sure how the properties of nth roots applies to my result. I wasn't sure how to type out the radical sign so I scanned my answer. The placement of the negatives is messing me up. The fact that the nth root is 5 (odd) means the resulting...
11. ### Find intercept with radicals

I'm getting ready for a test and don't want any surprises. I need to find any intercepts. I could a refresher. y = x ?16 -x^2
12. ### I need help with radicals!!

Hello everyone :roll: I'm taking college algebra and I need help in this rationalize the denominator 6/(2??7)
13. ### Simplifying radicals in denominator

I get the general concept of simplifying radicals in denominator or rationalizing them, but some problems I'm a little iffy on. I just need someone to check if my answers are correct. I'm not sure if I am doing these problems the correct way. 1. (7?72)/?40 Answer I got: (21?5)/5 2...
14. ### Problem with radicals in the denominator

Hi, I am an adult self-learner and I am having a problem with the solution to an exercise in my textbook. Perhaps you can help me. I have this problem to solve: $\frac{{a - b}}{{a\sqrt b - b\sqrt a }}$ And I am following the following steps: (1) \[\frac{{a - b}}{{a\sqrt b - b\sqrt a }}...
15. ### An equation with radicals and a real parameter

Hello! To solve the equation \sqrt[3]{x+1}-\sqrt{x^2-1}=a where a\in R. Thank You!
16. ### Another equation with radicals

Hello! To solve the equation \sqrt[3]{x+1}+\sqrt2=0. Thank You!
17. ### An equation with radicals

Hello! To solve the equation \sqrt{x}-sqrt{y}=1 where x,y\in N*. Thank You!