Question

what is the exact value of the expression?

Answer 1

\[\sqrt{45}-\sqrt{75}+\sqrt{192}\]

Answer 2

\[ \large \sqrt{45}=\sqrt{5\cdot9}=3\sqrt{5} \]

Answer 3

do the same with the other roots.

Answer 4

for the sqrt75 i got sqrt5*7*2

Answer 5

im stuck there

Answer 6

i think \(75=25\times 3\)

Answer 7

right

Answer 8

ohh..makes sense

Answer 9

making \(\sqrt{75}=\sqrt{25\times 3}=\sqrt{25}\times \sqrt{3}=5\sqrt{3}\)

Answer 10

now do the same with 192

Answer 11

\[ \large \sqrt{192}= \]

Answer 12

would it be 4sqrt6?

Answer 13

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

Answer 14

oh okay. i missed a 2

Answer 15

so how would i simplify all that?

Answer 16

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

Answer 17

now combine like terms.

Answer 18

do you add or multiply?

Answer 19

add or substract

Answer 20

oh okay so 6 sqrt 11?

Answer 21

yeah

Answer 22

okay thx

Answer 23

\[ \large =3\sqrt{5}+3\sqrt{3}=3(\sqrt{5}+\sqrt{3}) \]