## LaurenAshley1201 3 years ago help :) multiply expression

1. LaurenAshley1201

$2\sqrt{6}\times \sqrt{10}$

2. Calcmathlete

Multiply them seperately... $2\sqrt6 \times \sqrt{10} \implies 2\sqrt{6 \times 10} \implies 2 \sqrt{2 \times 3 \times 2 \times 5} \implies~?$

3. Calcmathlete

Can you finish from there? Can you simplify the radical?

4. violy

|dw:1344751807375:dw| here is an example. :)

5. waterineyes

@merp it is better if you do it here by your own..

6. waterineyes

@LaurenAshley1201 $\implies 2 \sqrt{\color{blue}{\underline{2 \times 2}} \times 3 \times 5} = ??$

7. LaurenAshley1201

2 sqrt 60? i dont think im doing it right

8. waterineyes

You can solve further for $$\sqrt{60}$$..

9. LaurenAshley1201

2 sqrt 15

10. waterineyes

$\sqrt{60} = \sqrt{\color{blue}{\underline{2 \times 2}} \times 3 \times 5}$ Can you go further..??

11. violy

think of a perfect square number that can go into 60.

12. waterineyes

Yes..

13. waterineyes

There is one 2 outside too..

14. Calcmathlete

We have broken 60 down into prime factors for you. Remember this? $\sqrt{x \times x} = x$Use the same rule...

15. waterineyes

$2 \times 2 \sqrt{15} = ??$

16. violy

do you mean sqrt (4 * 15) ?

17. waterineyes

No..

18. LaurenAshley1201

i dont know how to go any furhter

19. waterineyes

$$\sqrt{60}$$ is how much ??

20. waterineyes

you have solved it above..

21. waterineyes

$\sqrt{60} = \sqrt{\color{blue}{\underline{2 \times 2}} \times 3 \times 5} = ??$

22. violy

its like sqrt( 5 x 5) = sqrt (25) = 5.

23. waterineyes

Where are you having problem @LaurenAshley1201

24. violy

let me give you an example: $\sqrt{45}=\sqrt{3*3*5}=\sqrt{9} * \sqrt{5} = 3\sqrt{5}$

25. LaurenAshley1201

sqrt of 60 is 2 sqrt 15

26. violy

you got it right now! :)

27. waterineyes

In square root you can pull out one from a pair like this: $\sqrt{4 \times 4 \times 5}$ Here you can see there are two 4's. SO you can take one 4 outside and there will remain no 4 in the square root brackets: So it becomes; $\sqrt{\color{green}{\underline{ 4 \times 4} \times 5}} \implies 4 \sqrt{5}$

28. Calcmathlete

Ok. Do you understand this at the very least? $\sqrt{3 \times 3} = \sqrt{3^2} = \sqrt{9} = 3\color{red}{\huge??????}$

29. LaurenAshley1201

yes i do

30. Calcmathlete

THat's basically what you're doing here, it's just that you can make sense of it without showing all of the steps because you know the end result which is why we know that$\sqrt{60} = \sqrt{2 \times 2 \times 3 \times 5} = 2\sqrt{15}$

31. waterineyes

$2 \sqrt{60} = 2 \times (2 \sqrt{15}) = ??$

32. LaurenAshley1201

@Calcmathlete would that be my final answer?

33. Calcmathlete

Not quite...you forgot the 2 that was already out there... $2 \times 2\sqrt{15} = ?$

34. violy

not yet, example: $3*(4\sqrt{5}) = 3*4\sqrt{5} = 12\sqrt{5}$

35. LaurenAshley1201

i figuired it out,with everyones help ! thanks everyone

36. Calcmathlete