[SOUND] Let's look at square root, additions and subtraction.

[SOUND] For example, let's add these two numbers together.

The first things we'll do is we'll simplify each of the square root terms by

extracting all perfect squares. In other words, this is equal to five

times the square root of nine times five. 45 = 9 * 5 and 9 is a perfect square,

and then, plus the square root of four times five,

20 4 * 5 and 4 is a perfect square. And now, by properties of radicals, this

is equal to, five times the square root of nine times the square root of five

plus the square root of four times the square root of five,

Which is equal to five times the square root of nine, which is three, times the

square root of five plus the square root of four, which is two, times the square

root of five, which is equal to 15 times the square root of five plus two times

square root of five. And finally, we can combine these.

If we have 15 square root of five plus two more, then we have 17 square root of

five, which would be our answer. All right, let's look at another example.

[SOUND] Let's simplify this. Again, let's start off by simplifying

each square root term by extracting all perfect squares.

In other words, we can write 27 as 9 * 3 and nine is a perfect square.

And then we can write 75 as 25 * 3 and 25 is a perfect square.

And finally we can write 12 as 4 * 3 and four is a perfect square.

Again, by properties of radicals, this is equal to the square root of nine times

the square root of three, and then plus three times the square root of 25 times

the square root of three minus two times the square root of four times the square

root of three, which is equal to the square root of nine

is three. So we have three times the square root of

three plus three times the square root of 25, which is five, times the square root