150 = 3x2x5x5

take the 5’s out

original 5 times 5 taken from inside = 25

2×3 = 6

sooooo 25 root 6

that stands for “five times the square root of 150”, the square root of a number means the number that when multiplied by itself will equal that number, in the case of 150, that number is

12.2474487, making the techniqual answer 61.237

However; before you write that down, I’m betting this lesson is actually on factoring. Factoring you make a factoring tree, you’ve probably done this, what you do is you take PRIME number, and divide the origonal number by it. then you take another PRIME number and divide the previous quotient by it.

for this one its 150 / 5 = 30 then 30 / 5 = 6 and finally 6 / 3 = 2 you’ve now factored it and you can check by multiplying them back, 5 x 5 = 25 25 x 3 = 75, 75 x 2 = 150. if you got the number you started with you did it right remember that every prime number

What does all this mean? you’ve now factored 150 so you could instead write this as 5√ 5 x 5 x 3 x 2, or 5√5(squared) x 3 x 2. Having a 5 squared in a square root makes no sense though, so why not take it out, making it 5 x 5√3×2, well now you have 5 x 5 outside of it, so why not just simplify that to 25?

making your final answer 25√3 x 2

25 X 6 =150. 25 is a perfect square and the root is 5. So take out the 25 and leave 6.

5 X 5√6=

25√6

There aren’t any other square roots within the number 6, so you have just fully simplified 5√150.

now you have 5*5*√6 or 25√6

if I followed this correctly