Solve by using Models that are square root function

Question

The formula v=√20L can be used to estimate the speed of a car, v, in miles per hour, based on the length, L, in feet, of its skid marks upon sudden braking on a dry asphalt road. If a car is involved in an accident and its skid marks measure 405 feet, at what estimated speed was the car traveling when it applied its breaks just prior to the accident? 

 

 

 

 

 

 

( the answer is: 90 mph but i need help step by step on how they got this answer)

Answer 1

v=√20L where L=405 feet

v=√(20*405)

v=√8100

8100=81*100

v=√81*√100

v=9*10

v=90 mph

in other words, 8100 is a perfect square, it is 90*90

you could have put √8100 into your calculator to get 90, or...

20*405=(2*2*5)*(5*81)=(2*2)(5*5)(9*9)

√(2*2)(5*5)(9*9)=2*5*9=90 again