Question

Help please its a very important question...

Answer 1

Part A: Use the properties of exponents to explain why \[16^\frac{ 1 }{ 4 }\] is called the fourth root of 16. (5 points)

Part B: The length of a rectangle is 5 units and its width is \[\sqrt{5}\] unit. Is the area of the rectangle rational or irrational? Justify your answer. (5 points)

Answer 2

\[
16^{\frac 14} = \sqrt[4]{16}
\]

Answer 3

yes ik tht but why?

Answer 4

Because \[
16^{\frac 14} = x
\]If we take both sides to \(4\)th power: \[
\left(16^{\frac 14}\right)^4 = x^4 \\
16^{1/4\times 4} = 16^1 =16
\]Then \[
16 = x^4
\]The inverse operation here would be: \[
\sqrt[4]{16} = x
\]So \[
16^{\frac 14} = x = \sqrt[4]{16}
\]

Answer 5

oh ok thank you! can you help me with part b?

Answer 6

Area of rectangle is length times width.

Answer 7

yes...

Answer 8

So what is the area? Then decide if it is irrational or not.

Answer 9

would you do \[^5\sqrt{5}\]

Answer 10

no, you just have \(5\sqrt{5}\)

Answer 11

that's irrational right?

Answer 12

yes

Answer 13

Thank You So Much!

Answer 14

@camerondoherty fan me plz

Answer 15

This is such an old question cx