## anonymous one year ago Simplify 3 square root of 5 end root minus 2 square root of 7 end root plus square root of 45 end root minus square root of 28.

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1. anonymous

2. jim_thompson5910

The expression is this right? $\large 3\sqrt{5}-2\sqrt{7}+\sqrt{45}-\sqrt{28}$

3. anonymous

do you know how to solve it?

4. jim_thompson5910

first we need to simplify $$\Large \sqrt{45}$$

5. jim_thompson5910

$\large \sqrt{45}=\sqrt{9*5}$ $\large \sqrt{45}=\sqrt{9}*\sqrt{5}$ $\large \sqrt{45}=3\sqrt{5}$

6. jim_thompson5910

Notice how I factored it into 9*5 one of the factors is the largest perfect square factor possible

7. jim_thompson5910

make sense?

8. anonymous

yes

9. jim_thompson5910

how would you simplify $$\Large \sqrt{28}$$ ?

10. anonymous

2 square root of 7

11. jim_thompson5910

good

12. jim_thompson5910

So $\large 3\sqrt{5}-2\sqrt{7}+\sqrt{45}-\sqrt{28}$ turns into $\large 3\sqrt{5}-2\sqrt{7}+3\sqrt{5}-2\sqrt{7}$

13. jim_thompson5910

from here combine like terms

14. anonymous

ok

15. anonymous

i dont really know how to do this part its confusing

16. jim_thompson5910

if I gave you something like 3x+7y+2x+10y, would you be able to combine like terms?

17. anonymous

yes

18. anonymous

it would be 5x + 17y right?

19. jim_thompson5910

yes that's correct

20. jim_thompson5910

you'll use the same idea

21. jim_thompson5910

let x = sqrt(5) and y = sqrt(7) $\large 3\color{red}{\sqrt{5}}-2\color{blue}{\sqrt{7}}+3\color{red}{\sqrt{5}}-2\color{blue}{\sqrt{7}}$ $\large 3\color{red}{x}-2\color{blue}{y}+3\color{red}{x}-2\color{blue}{y}$

22. anonymous

ok

23. jim_thompson5910

simplify 3x-2y+3x-2y to get ???

24. anonymous

6x-y?

25. jim_thompson5910

6x is correct -y is not

26. anonymous

ok

27. jim_thompson5910

try again

28. anonymous

29. jim_thompson5910

-2y-2y is -4y, agreed?

30. jim_thompson5910

$\large 3\color{red}{x}-2\color{blue}{y}+3\color{red}{x}-2\color{blue}{y}$ $\large 6\color{red}{x}-4\color{blue}{y}$ $\large 6\color{red}{\sqrt{5}}-4\color{blue}{\sqrt{7}}$

31. jim_thompson5910

So, $\large 3\sqrt{5}-2\sqrt{7}+\sqrt{45}-\sqrt{28} = 6\sqrt{5}-4\sqrt{7}$

32. anonymous

ok thank a lot

33. anonymous

can you help me with this one please? if you want to. Which statement is true about the difference 2 square root of 7 − square root of 28?

34. jim_thompson5910

$2\sqrt{7} - \color{red}{\sqrt{28}} = 2\sqrt{7} - \color{red}{2\sqrt{7}} = 0\sqrt{7} = 0$