Question

Part A: Use the properties of exponents to explain why 16 raised to the power of 1 over 4 is called the fourth root of 16. (5 points)

Part B: The length of a rectangle is 5 units and its width is square root of 5 unit. Is the area of the rectangle rational or irrational? Justify your answer. (5 points)

Answer 1

I would really appreciate some help with this. I have trouble with radicals and if someone could explain this question to me and help me answer it I'd be really grateful!

Answer 2

\(\bf a^{\frac{n}{m}} = \sqrt[m]{a^n}\qquad thus\\\quad \\
16^{\frac{1}{4}}\implies \sqrt[4]{16}\\ \quad \\
16\implies 2\times 2\times 2\times 2\implies 2^4\qquad thus\\ \quad \\
\sqrt[4]{16}\implies \sqrt[4]{2^4}\implies 2\)

thus "2" is a number that when multiplied FOUR TIMES by itself is 16, thus the FOURTH ROOT

Answer 3

Thank you so much!! Could you help me with Part B?

Answer 4

is it an irrational number? well, check for yourself --> http://www.mathsisfun.com/irrational-numbers.html