Assalamualaikum warahmatullahi wabarakatuh.
Welcome to subtopic 1.2.
In this subtopic, we will be discussing
surds.
By the end of this subtopic,
you should be able to define surds and
express it into its simplified form.
You should also know how to perform basic
operations such as addition, subtraction
multiplication and division on surds.
and lastly you should be able to solve
equations involving surds.
Let's start with the definition of surds.
A surd is a nth root of a number
that has a irrational value.
Irrational is a decimal values that has endless non repeating digits.
The example will explain this better.
For example, square root of 2. Square root of 2 can also be written like this.
See without the number of root written with it.
If we calculate this this is equal to 1.41421356237 and the number goes on infinitely.
This is an irrational number and because
of that square root of two is a SURD.
But if I have square root of 4, we know
that this is equal to 2 and
since 2 is not an irrational number therefore square root of 4 is not a surd.
Bear in mind that surd is not just for square root.
From the definition. We know that surd could be from any root.
To take the cube root of 3 this is
equal to 1.44224 and so on.
Is this a surd? The answer is yes.
Let's try once more and then we'll move on the cube root of 8. is this a surd?
The answer is no because cube root of 8
is equal to 2.
Hopefully, this is enough explanation.
If you are still confused, you can
discuss this more in your tutorial session.
Moving on our next objective is to simplify surds. Mainly in this chapter,
after we are going to use square root as
our surds and because of that I'm going
to introduce a term for you that is
called perfect square.
Perfect square is a number from Square.
For example,
1 squared
2 squared
3 squared
4 squared
and so on.
So one squared is equal to 1.
2 squared is equal to 4.
3 squared is equal to 9 and
4 squared is equal to 16.
Now, this is what we All perfect square
The same goes for 25
36
49
64
81
a hundred
and so on.
Let's test you .
Is a 144 a perfect square.
The answer is yes, because 12 squared is
equal to 144.
One more test and then we'll move on.
Is 50 a perfect square?
The answer is no. Now we can proceed.
To simplify surds, take a look at the
first example here.
The first one is square root 24.
First thing to do is to list out its
factors.
The factors of 24 is 1 with 24, 2 with
12, 3 with 8 and 4 with 6
and among this list
We need to recognize which pair has the
perfect square.
Now this one has perfect square in it.
Let me make this one smaller
so we can rewrite this as Square root of
4 x 6 and because they are in
multiplication we can separate them to
become the square root of 4 multiplied
by the square root of 6.
So 2 Square Root 6 is the simplified form
of the square root of 24, right.
So, let's see another example here square
root of 50.
Our first step is to list the factors.
So the factors of 50 is 1 with 50
2 with 25 or look now.
We've seen the perfect square here.
And again, let me make this one smaller.
So let me rewrite this as square root of
25 x 2 and because they are in multiplication
We can split this to be square root 25 multiplied by square root of 2.
We know that square root 25 is equal to 5 and square root of 2.
I'm going to leave this two questions for
you.
Pause this video now and continue when you are done. Finished......
Let's check your answers square root of
98.
The first thing that you need to do is to
list out its factor.
Second thing that you need to do is to recognize its perfect square.
So square root 98 can be rewrite as
square root of 49 multiplied by 2 and
then split them
we're going to get square root of 49 x
square root of 2 simplify more.
This one will become 7 square root of 2
For question d,
I'm just going to write the answer. The
answer for this one is 6 square root of 3.
Very well, so that's it for this
video. In the next video,
We will be discussing the rules of surds. They are quite similar to indices, so it
should be very easy to do.
Thank you for your attention.
Have a great day and take care.
