## anonymous 4 years ago HOW DO I FIGURE THIS OUT $6\sqrt{2} - 3\sqrt{2}$

1. KingGeorge

$6\sqrt{2} - 3\sqrt2 = \sqrt{2} \cdot (6-3) =3\sqrt2$

2. anonymous

how do i do these? $\sqrt{90} , \sqrt{125}, 4\sqrt{20}$

3. KingGeorge

What do you want to do with them? Just simplify them as much as possible?

4. anonymous

no have an anser like $9\sqrt{10} or 10\sqrt{9} examples$

5. anonymous

This one i dont get either $5\sqrt{10} * 3\sqrt{?}$

6. anonymous

i ment to put * $3\sqrt{8}$

7. KingGeorge

Let's start with the first one.$\sqrt{90} = \sqrt{9} \cdot \sqrt{10} = 3\sqrt{10}$similarly, $\sqrt{125} = \sqrt{25} \cdot \sqrt{5} = 5\sqrt5$and$4\sqrt{20} = 4\sqrt{4} \cdot \sqrt5 = 4 \cdot 2 \cdot \sqrt5 = 8\sqrt5$

8. anonymous

$7\sqrt{72}$

9. KingGeorge

As for that last problem, $5\sqrt{10} \cdot 3\sqrt8 = 15 \cdot \sqrt{10} \cdot \sqrt8 = 15 \cdot \sqrt{80}=15 \cdot \sqrt{16} \cdot \sqrt5 = 60\sqrt5$Is it clear what you have to do for these problems now?

10. anonymous

i dont get the one i posted or the 4/20 one.

11. anonymous

would this one $\sqrt{8} * \sqrt{3}$ = $\sqrt{24}$?

12. anonymous

would this one $\sqrt{8} * \sqrt{3}$ = $\sqrt{24}$?

13. KingGeorge

That would be correct. Good job! As for the other problems, give me a few more seconds to finish typing up the response...

14. anonymous

KK :)

15. KingGeorge

Well, both the 7/72 and 4/20 are basically the same problem with different numbers. You have an expression with some number outside the radical (4 and 7), and a number inside (20 and 72). At the beginning, you can just ignore the number outside. Then simplify the radical as much as possible. In this case, $\sqrt{72} = \sqrt{36} \cdot \sqrt2 = 6\sqrt2$and $\sqrt{20} = \sqrt4 \cdot \sqrt5 =2\sqrt5$Then, to finish it all off, you multiply by the number you originally had in front. So,$7\sqrt{72}=7\cdot(6\sqrt2) = 42\sqrt2$$4\sqrt{20}=4\cdot (2\sqrt5)=8\sqrt5$And those would be the final answers. Also, with the square root of 24, it would be better to then simplify like so$\sqrt{24} = \sqrt4 \cdot \sqrt6 = 2\sqrt6$

16. anonymous

i see... ok. Thanks so much!

17. KingGeorge

Could you now simplify $4\sqrt{45}$just for a little bit more practice?