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Get ready for an exciting dose of math.
Find the value of this square root
without using a calculator. At first,
you will look at this square root of 49
and you will think, "Huh, this is easy."
The square root of 49 is 7. But then you
will look at this square root of 48 and
your brain might say, "Wait, how am I
supposed to find its square root?" But
don't worry, let's solve it step by
step. First we deal with the inner part
which is the square<unk> of
49us<unk> of 48. We already know that
the square<unk> of 49 is 7. Now let's
break that seven down in a clever way.
Let's write 7 as 4 + 3. 4 is 2^ 2. And
well 3 is just square<unk> of 3 squared.
So that makes it 2^ 2 +<unk> of 3^ 2.
Noise. Next, let's look at the
square<unk> of 48. That's not a perfect
square, but it can be broken down. 48 is
16 * 3. And 16 is 4 * 4. So now the
square<unk> of 48 becomes the
square<unk> of 4 * 4 * 3. Now we can
write it as square<unk> of 4 *<unk> of 4
*<unk> of 3. Write both these square
roots of 4 as 2 and keep this
square<unk> of three as it is. Therefore
using this and this the square<unk> of
49 minus the<unk> of 48 can be written
as 2 ^2 +<unk> 3^ 2 - 2 * 2 *<unk> 3.
Oh, can you notice something? Yeah, this
is of the form a^ 2 + b^ 2 - 2 a which
is none other than a - b square. So this
will become the 2 - square<unk> of 3
square. Now if we take square root on
both sides this will become our original
expression and this square will be
cancelled with this square root and it
will become simply 2 minus square<unk>
of 3 and that's it. We know that the
square root of 3 is
1.732 and thus this will become 268.
No, good.
[Music]
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