Question

1. Part A: Use the properties of exponents to explain why 64^1/2 is called the square root of 64.

Answer 1

A: When you multiply two numbers, their exponents add. 
So, $64^{\frac{1}{2}} * 64^{\frac{1}{2}} = 64^{\frac{1}{2} + \frac{1}{2}} = 64^{1} = 64$

Since 64^1/2 multiplied by itself is 64, then it is the square root of 64.

B: The area is irrational. 7 * √7 is irrational.

Answer 2

1.  
64^1/2 * 64^1/2  = 64^(1/2 + 1/2) = 64^1  = 64

2. Area = l * w  = 7 * √7  =  7√7

√7 is irrational  so 7√7 is irrational also