## kiamonstaa 3 years ago what is the exact value of the expression?

1. kiamonstaa

$\sqrt{45}-\sqrt{75}+\sqrt{192}$

2. helder_edwin

$\large \sqrt{45}=\sqrt{5\cdot9}=3\sqrt{5}$

3. helder_edwin

do the same with the other roots.

4. kiamonstaa

for the sqrt75 i got sqrt5*7*2

5. kiamonstaa

im stuck there

6. satellite73

i think $$75=25\times 3$$

7. helder_edwin

right

8. kiamonstaa

ohh..makes sense

9. satellite73

making $$\sqrt{75}=\sqrt{25\times 3}=\sqrt{25}\times \sqrt{3}=5\sqrt{3}$$

10. helder_edwin

now do the same with 192

11. helder_edwin

$\large \sqrt{192}=$

12. kiamonstaa

would it be 4sqrt6?

13. helder_edwin

i got $\large \sqrt{192}=\sqrt{2^6\cdot3}=2^3\cdot\sqrt{3}=8\sqrt{3}$

14. kiamonstaa

oh okay. i missed a 2

15. kiamonstaa

so how would i simplify all that?

16. helder_edwin

now plug in everything: $\large \sqrt{45}-\sqrt{75}+\sqrt{192}=3\sqrt{5}-5\sqrt{3}+8\sqrt{3}$

17. helder_edwin

now combine like terms.

18. kiamonstaa

19. helder_edwin

20. kiamonstaa

oh okay so 6 sqrt 11?

21. goformit100

yeah

22. kiamonstaa

okay thx

23. helder_edwin

$\large =3\sqrt{5}+3\sqrt{3}=3(\sqrt{5}+\sqrt{3})$