How to simplify this fractional surd

Added: 2026-05-09

[00:00:00]Let me show you how to solve this math question on the board.

[00:00:04]The question says simplify<unk> 5 + roo<unk> 5 / <unk>2.

[00:00:13]If you want to solve this question correctly, you need to make use of something called rationalization of sort.

[00:00:20]And how is it done? Let me show you.

[00:00:24]Here's the solution.

[00:00:27]First of all, let us write down what is given to us.

[00:00:30]we have<unk> 5 +<unk> 5 / <unk>2.

[00:00:37]Now to perform rationalization we need to create another fraction using this denominator this roo<unk>2. So we need to create another fraction which is <unk>2 / <unk>2.

[00:00:53]After that we are going to use this fraction that we have created to multiply the fraction that was already here. So that means we are going to have this.

[00:01:04]You understand? Now let us multiply what we have this roo<unk>2 here. We multiply each of the terms inside this bracket each of these numbers inside this bracket. So <unk>2 *<unk> 5 that give us roo<unk> 10 because um 2 * 5 will give us 10. So we have roo<unk> 10.

[00:01:27]You understand? Plus this roo<unk>2 here times this other roo<unk> 5. We going to have another roo<unk> 10.

[00:01:36]Have root 10 because 2 * 5 will give us 10 and both of them are inside square root sign.

[00:01:42]That's why the 10 has to be inside the square root sign. You understand? Then divided by <unk>2 * <unk>2.

[00:01:52]Anytime you're multiplying the same numbers that are inside square root sign like we have these two and these two are inside square root signs and both of them are being multiplied together. The answer will be equal to one of them. The answer will be equal to one of the numbers without the square root sign anymore.

[00:02:10]You understand? If you have something like this roo<unk>3 * another roo<unk>3 the same numbers inside square root sign the answer will be equal to one of these numbers without the square root sign anymore.

[00:02:27]So that's how we got to this point.

[00:02:30]If you understand what I have done here type I understand in the comment section.

[00:02:34]Now if you look at the numerator you can see that we have the same numbers inside the square sign. That means we can add them. We can go ahead and add. If they're not the same, we cannot add.

[00:02:46]You understand? So, let us add these two numbers.

[00:02:50]How do we add these two numbers? Take note, if you want to add, there are we make use of the numbers in front here.

[00:02:57]But there is no visible number here.

[00:03:00]Anytime you don't see a visible number here, it means the number is one. So, this is something as saying 1<unk> 10 + 1<unk> 10. That will give us what? 2 root 10 that one here plus the one here the invisible one here that will give us two.

[00:03:17]Then we pick one of these root 10.

[00:03:22]Understand? Then divided by this two.

[00:03:27]Now over here two will cancel two. This two cannot divide this 10 because this 10 is inside square to sign. It can only divide this two in front. So two cancel two and we are left with roo<unk> 10. And this is the answer to this question. If you find this video interesting, let me know in the comment section.