You've got this number, 10√125, and it looks a bit... much. Like a complicated knot you're not sure how to untangle. But honestly, simplifying square roots is a bit like finding the most efficient way to pack a suitcase – you want to make things as neat and compact as possible.
So, let's talk about that √125 part. The goal here is to pull out any 'perfect squares' from inside the square root symbol. Think of perfect squares as numbers that are the result of squaring a whole number – like 4 (2x2), 9 (3x3), 16 (4x4), and so on. If we can find a perfect square that divides evenly into 125, we can simplify things.
What divides into 125? Well, 5 is a factor, right? 125 divided by 5 is 25. And hey, 25 is a perfect square! It's 5 times 5.
This is where a handy rule comes in: √ab = √a × √b. It means we can split up a square root into the product of two square roots. So, √125 can be rewritten as √(25 × 5).
Now, using that rule, we can separate it: √25 × √5.
We know the square root of 25 is a nice, clean 5. So, that part becomes just 5.
We're left with 5 × √5. The number 5 inside the square root doesn't have any perfect square factors (other than 1, which doesn't help us simplify), so √5 is as simple as it gets.
Putting it all back together with the original 10 we had at the front: we have 10 multiplied by our simplified √125, which is 5√5.
So, 10 × (5√5) = 50√5.
And there you have it. 10√125, which might have looked a bit daunting, is now a much friendlier 50√5. It's the same value, just presented in a more streamlined way, making it easier to work with and understand.
