Algebra 1: Square Root in simplest radical form

How do I find the square root in simplest radical form?
Please no rude answers, if you know it then thank you if you don't, dont comment please :)
(theres no square root button on the keyboard so i just wrote the words square root)


Square root of 1800

square root of 464

square root of 780

5 square root 60 x 3 square root 56

The key to solving these types of problems is to factor the number within the rad sign and then simplifying. Always look for perfect squares as factors, e.g., 4, 9, 16, 25, 36, 49, 64, 81, 100, 400, 900, etc.


(1) √1800 = √900 √2 = 30 √2

You could have also solved this problem by factoring using perfect squares 100 or less (in case √900 didn't come to mind as a perfect square):

√1800 = √100√18 = √100√9√2 = (10)(3)√2 = 30 √2


(2) √464 = √16√29 = 4 √29

Here's another way (in case it wasn't obvious that 464 was divisible by 16):

√464 = √4√116 = √4√4√29 = (2)(2)√29 = 4 √29


(3) √780 = √4√195 = 2√13√15


(4) 5√60 x 3√56 = 5√4√15 x 3√4√14 = (5)(2)√15 x (3)(2)√14 = 10√15 x 6√14 = 60√210 = 60√2√3√5√7



Hope this helps...good luck!