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

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) (Show Source): You can put this solution on YOUR website!
Problem #1
If we have

Then we are asking: what number multiplied by itself 4 times equals 16? In other words:

So if we take the negative fourth root of 16 with a calculator, we get

Since -2 can be represented by a fraction (ie ) it is a rational number.

Problem #2

Rewrite the square root of a product as a product of square roots (ie )
Since any root can be written as a fractional power (ie rewrite the square roots as exponents of 1/2.
Multiply the exponents
So this is your simplified answer. It can also be written as:

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