kiamonstaa
what is the exact value of the expression?



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

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

helder_edwin
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do the same with the other roots.

kiamonstaa
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for the sqrt75 i got sqrt5*7*2

kiamonstaa
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im stuck there

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

helder_edwin
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right

kiamonstaa
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ohh..makes sense

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

helder_edwin
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now do the same with 192

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

kiamonstaa
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would it be 4sqrt6?

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

kiamonstaa
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oh okay. i missed a 2

kiamonstaa
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so how would i simplify all that?

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

helder_edwin
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now combine like terms.

kiamonstaa
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do you add or multiply?

helder_edwin
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add or substract

kiamonstaa
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oh okay so 6 sqrt 11?

goformit100
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yeah

kiamonstaa
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okay thx

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