Question

BE PATIENT!
Question Below:

Answer 1

\[\sqrt{150b^3} \]

How would you go about finding the Largest Perfect Square?

Answer 2

@UnkleRhaukus @phi @mathstudent55 @bahrom7893 @jim_thompson5910

Answer 3

BTW that is a 3 not 2 :)

Answer 4

\(150=25\times 6\) is a start

Answer 5

Yes but what is a good method to find the largest Perfect Sqaure?

Answer 6

I don't understand your question, can you clarify?

Answer 7

Like what is a good method to quickly and efficiently find the "Largest Perfect Square" (the factors)

Answer 8

Estimation, guess and check. Thats what I would do, anyway. You should know the perfect squares at least up to 20^2, they become very handy.

Answer 9

Interesting, I will commit it to memory then :) I just thought there was a faster way but thanks anyways now I know there are no shortcuts xD

Answer 10

I'm not saying there are none, there very well could be a faster method, but I've never used anything else. Although I've never really been in the situation of solving something like this with numbers that high anyway

Answer 11

Oh ok thanks anyways :D I will stick to the usual method until I get a tip from someone xD

Answer 12

factor

Answer 13

Yes but there are so many possibilities and only a few lead to something other than a decimal.

Answer 14

If you really wanted to, you could find the prime factorization of the value under the radical, so you could look at all the square roots...For example, if you had say 252, the prime factorization would be
\[2^2 \times 3^2 \times 7\]So you know that the largest perfect square factor of 252 is (2 times 3)^2 = 6^2 = 36

Answer 15

O_O too much info xD but knowing what you previously stated I can somehow form a small system now. I just thought there was a system.

Answer 16

The closest I can think of to a system to figure out the largest perfect square factor is to find the prime factorization

Answer 17

Nope,you're just factoring whatever you can out of the square root, like @satellite73 mentionedand @vinnv226 demonstrated.

Answer 18

Yes but prime factorization takes a while compared to this, and @Jhannybean there are just so many different ones to choose it's hard to find the right one quickly.

Answer 19

\[\large \sqrt{150}= \sqrt{\color{red}{25}\cdot \color{blue}{6} \cdot \color{green}{b^2}\cdot b} = \sqrt{ 5^2 \cdot 3 \cdot 2 \cdot b^2 \cdot b} = 5b\sqrt{6b}\]

Answer 20

@JA1 I'm not sure what level of math you're in right now, but as you progress, you'll hopefully get a better "feel" for numbers and estimating square roots will become more comfortable. It helps to memorize some "benchmark" square roots to help you. I'd suggest you know the squares up to 20 squared, and I'd keep in mind 30^2, 40^2, 50^2, and so on (these are easy to compute by hand, you don't need to memorize them) and then from there you can figure out a certain "range" that the square root is in. This will help you pick which squares might factor out.

Answer 21

8th grade moving out to 9th grade now, I get the concept and how to do it, I have that natural feel for it but sometimes I get stuck on little hings, but hey, that's what OS is for :)

Answer 22

Right, practice will help you in these kind of problems, so I wouldn't sweat it

Answer 23

Yah little by little I can amass a vast amount of numbers that are commonly used and won't need to think twice about what square to use :)