Question

Can you help? A medal will be given! :3

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.

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.

Answer 1

Part A
\(\Huge 64^{\frac{1}{2}}=(8×8)^{\frac{1}{2}} \)
now for the properties of exponents we chose the have numbers of them
so
\(\Huge 64^{\frac{1}{2}}=(8×8)^{\frac{1}{2}}=8=\sqrt{64} \)

Answer 2

part B

\(\Huge\text{ the area = length × width}\)
\(\Huge\text{ the area} = 7 ×\sqrt {7}=\color{red}{7\sqrt7}=7^{\frac{3}{2}}\)

so its irrational , u cant write \(7^{\frac{3}{2}}\) as \(\frac{a}{b}\) formula

Answer 3

got it ?
if not , just let me know :D

Answer 4

I got it, thank you so much :3

Answer 5

np ur wlc ^^

Answer 6

wait, for part A, why is it a square root?

Answer 7

becuz , u chose one of two ^^

Answer 8

OOOOh, ok, thanjs