SOLUTION: d.. Problem #1 Can someone explain to me if the following is rational or irrational and why? minus then an index of 4 sqrt 16 Problem #2 Simplify. Assuming all varia

Algebra ->  Radicals -> SOLUTION: d.. Problem #1 Can someone explain to me if the following is rational or irrational and why? minus then an index of 4 sqrt 16 Problem #2 Simplify. Assuming all varia      Log On


   

Question 76330: d..
Problem #1
Can someone explain to me if the following is rational or irrational and why?
minus then an index of 4 sqrt 16

Problem #2
Simplify. Assuming all variables represents positive numbers
sqrt (x^4y^3)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Problem #1
If we have
-root%284%2C16%29
Then we are asking: what number multiplied by itself 4 times equals 16? In other words:
x%2Ax%2Ax%2Ax=x%5E4=16
So if we take the negative fourth root of 16 with a calculator, we get
-root%284%2C16%29=-2
Since -2 can be represented by a fraction (ie -2=-2%2F1) it is a rational number.

Problem #2
sqrt+%28x%5E4y%5E3%29
sqrt+%28x%5E4%29%2Asqrt%28y%5E3%29 Rewrite the square root of a product as a product of square roots (ie sqrt%28xy%29=sqrt%28x%29sqrt%28y%29)
%28x%5E4%29%5E%281%2F2%29%2A%28y%5E3%29%5E%281%2F2%29Since any root can be written as a fractional power (ie root%28n%2Cx%29=x%5E%281%2Fn%29 rewrite the square roots as exponents of 1/2.
%28x%5E%284%2A%281%2F2%29%29%29%2A%28y%5E%283%2A%281%2F2%29%29%29 Multiply the exponents
%28x%5E2%29%2A%28y%5E%28%283%2F2%29%29%29 So this is your simplified answer. It can also be written as:
%28x%5E2%29%2Asqrt%28y%5E3%29%29%29