Question

Please help


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)

Answer 1

@greenlegodude57 @undeadknight26 @mathmale

Answer 2

We could work backwards:

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)" Use the fact that \[\sqrt[n]{x}=x ^{\frac{ 1 }{n }}\]

Answer 3

so we would be using the Rational Exponent Property?

Answer 4

to rewrite \[\sqrt{x} \] in the form \[ x ^{\frac{ 1 }{ n }}\]

Answer 5

Yes.

Answer 6

so would the answer be 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 it to 64 1/2

Answer 7

@mathmale