Question

Kate thinks of a number. She squares it, takes away the square root of 64, divides it all by the cube root of 512, and then finally she adds 8 quarters. Her answer is 4. What number did she start with?

Answer 1

Kate Started with √24

Step-by-step explanation:

Let say Kate thinks of a number  = N

Kate squares it  = N²

takes away the square root of 64  = N² - √64

= N² - 8

divides it all by the cube root of 512 = ( N² - 4) / √512

=  ( N² - 8)  / 8

she adds 8 quarters

=  ( N² - 8)  / 8   + 8(1/4)

= ( N² - 8)  / 8 + 2

( N² - 8)  / 8 + 2  = 4

=>  ( N² - 8)  / 8  = 2

=> N² - 8 = 16

=> N² = 24

=> N = √24

Kate Started with √24