what is the exact value of the expression?

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what is the exact value of the expression?

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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\[\sqrt{45}-\sqrt{75}+\sqrt{192}\]
\[ \large \sqrt{45}=\sqrt{5\cdot9}=3\sqrt{5} \]
do the same with the other roots.

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Other answers:

for the sqrt75 i got sqrt5*7*2
im stuck there
i think \(75=25\times 3\)
right
ohh..makes sense
making \(\sqrt{75}=\sqrt{25\times 3}=\sqrt{25}\times \sqrt{3}=5\sqrt{3}\)
now do the same with 192
\[ \large \sqrt{192}= \]
would it be 4sqrt6?
i got \[ \large \sqrt{192}=\sqrt{2^6\cdot3}=2^3\cdot\sqrt{3}=8\sqrt{3} \]
oh okay. i missed a 2
so how would i simplify all that?
now plug in everything: \[ \large \sqrt{45}-\sqrt{75}+\sqrt{192}=3\sqrt{5}-5\sqrt{3}+8\sqrt{3} \]
now combine like terms.
do you add or multiply?
add or substract
oh okay so 6 sqrt 11?
yeah
okay thx
\[ \large =3\sqrt{5}+3\sqrt{3}=3(\sqrt{5}+\sqrt{3}) \]

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