Question

HELP FAN AND METAL

Part A: Use the properties of exponents to explain why 64 raised to the power of 1 over 2 is called the square root of 64. (5 points)

Part B: The length of a rectangle is 7 units and its width is square root of 7 unit. Is the area of the rectangle rational or irrational? Justify your answer. (5 points)

I know for Part A I have to use the Rational Exponent Property, so would this be the answer for part A?
Where a number is raised to a fraction it can be converted to a radical. The 2 in 2√64 would become the denominator and a 1 would be the numerator changing

Answer 1

idk how to explain part A, I usually take that as a rule when I face it :)

For part B --
For the rectange, the area is the product of width and length.
In your case the area would (therefore) be \(\color{blue}{ 7\sqrt{7} }\)
and knowing that \(\color{blue}{ \sqrt{7} }\) is IRrational....

I don't think number is a is a fraction, don't confuse a "square root of a fraction" with this.

Answer 2

last sentence should say number \(\color{red}{ 1 }\)

Answer 3

So is B just irrational and why?

Answer 4

B/c the decimal of \(\color{purple}{ \sqrt {7} }\) is not repeating.

Answer 5

I mean if you would plug \(\color{purple}{ \sqrt {7} }\) into your calc and solve.

Answer 6

ok, and for Part A is my answer correct?

Answer 7

I don't really get what you meant. can you write it out for me using equation editor or by drawing (whichever you like more)

Answer 8

for Part A it is asking why \[64 \frac{ 1 }{ 2 } \] is called \[\sqrt{64}\]

Answer 9

you mean \[\huge\color{blue}{ 64^\frac{1}{2}=\sqrt{64} } \]

Answer 10

yea

Answer 11

Well, I can't really explain. For me it just a definite common sense, as a rule -

\[\huge\color{red}{ A^\frac{x}{v}=\sqrt[v]{A^x} } \]

Answer 12

The thing I dont understand it I know if lets say \[\sqrt[3]{55}\]= ?
I know it would be \[55 \frac{ 1 }{ 3 }\] because the 3 turns into the denominator but for this problem I dont understand where the 2 comes from

Answer 13

@SolomonZelman

Answer 14

never mind I figured it out

Answer 15

what did u end up getting for it? @FMA