How to simplify surd#maths #education #surd

Added: 2026-05-18

[00:00:00]Let's simplify this expression we have on the board together. So, we have root of 18 divided by 75. This is I can separate this and have root 18 divided by root 75.

[00:00:18]They are the same thing, okay? So, this is equal to you look for two numbers that when you multiply it will give you 18 and one must be a perfect square, okay? So, we have 9 * 2. 9 * 2 is what?

[00:00:32]18.

[00:00:33]And 9 is a perfect square. We are doing this because 18 is not what? A perfect square. So, we need to simplify it further, okay? Now, this is divided by root of 25 * 3. 25 * 3 will give you 75 and 25 is a perfect square. Now, this is equal to root 9 is what? 3.

[00:00:54]Root 2, okay? What is square root of 25?

[00:00:58]5. You write it outside the root 3, okay? Now, we are not done because we cannot leave this square root at the denominator. It is not normal. What do you do? You multiply both the numerator and the denominator by this to rationalize it. So, this is times 5 root 3 divided by 5 root 3. 5 root 3 divided by 5 root 3 is 1.

[00:01:23]So, it's just the same thing as multiplying by 1, which will not change this, okay? All right. So, 3 root 2 * 5 root 3 now will give us 3 * 5 is 15.

[00:01:36]Then root 2 * root um 3 will give you root 2 * 3, which is 6. Divided by 5 * 5 is 25. You have 25.

[00:01:48]Root 3 * root 3 is the same thing as root 3 squared, okay? So, this will cancel this and we are left with 3 * three. Now we can cancel. Five will divide 25 giving us five. Five here, three. Three cancel three, one. Three here, one. So we are left with At the numerator, we are left with root six. Then divided by the denominator which is five. And this is our final answer. Thank you for watching. Bye.