Question

explain... Solve

Answer 1

Take a look at the square root of 18. Perhaps we can split that into being multiplied by two terms? What are two pretty common terms that when multiplied give 18?

Answer 2

6*3

Answer 3

Good call. Now, try again and find a factor that is a perfect square. Neither 6 nor 3 fits this bill.

Answer 4

What is the largest perfect square to go into 18?

Answer 5

Righto. You need a perfect square that multiplies with another term to get 18. Anything come to mind? (Examples of perfect squares can be 16, 81, 4, ect.)

Answer 6

\(5\sqrt{2}\) cannot be further simplified however \(\sqrt{18}\) can be simplified more.

the factors of 18 are -- 1, 2, 3, 6, 9, 18
i suggest you to take a factor that is a perfect square of 18 (like 9) and we know 9 x 2 = 18.
so now we have \(\sqrt{9 \times 2}\). what is the square root of 9?

Answer 7

11.313708499

Answer 8

wait im confused

Answer 9

ohh iits 3

Answer 10

Yes! Now, where does that 3 go?

Answer 11

idk..

Answer 12

\[3\sqrt{2}\] is where that 3 would go since the radical basically "undid" the perfect square

Answer 13

so now what do you have, in total?

Answer 14

im still kinda confused

Answer 15

i think its b

Answer 16

Ok so you had \[5\sqrt{2}\] first right? and now we just found the new form of \[\sqrt{18}\] which is \[3\sqrt{2}\] so now we add them together.

Answer 17

What do the two radicals from the top and bottom have in common?

Answer 18

the both have 2

Answer 19

Yes! Exactly. So, now you notice that they both have the common value 2 underneath the radical. So they're both common. This lets us do what with the 3 and 5?

Answer 20

add them?

Answer 21

ding ding ding

Answer 22

So what would it look like then?

Answer 23

Not quite. What was common again?

Answer 24

the 2

Answer 25

Right. So it stays the same when you add the 3 and 5.

Answer 26

ohhh

Answer 27

Yes!

Answer 28

thanks :)

Answer 29

That is as simplified as it gets. Alternatively if you pop that into the calculator, it's 11.3 rounded to the nearest tenth.

Answer 30

@tkhunny could you correct me when I use the wrong words in my explanations? My mathematical terminology isnt the greatest T_T

Answer 31

@raven45 no problem!