Mathematics
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OpenStudy (imsleeziboii):
Help
10 years ago
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RhondaSommer (rhondasommer):
hi
10 years ago
OpenStudy (imsleeziboii):
hi
10 years ago
RhondaSommer (rhondasommer):
what u need help on?
10 years ago
OpenStudy (imsleeziboii):
A farmer needs to fertilize a large rectangular field. He knows the width of the field is \[\frac{ 50\sqrt{3} }{ \sqrt{2} }\] yards and the length is \[\frac{ 80\sqrt{5} }{ \sqrt{3} }\]. What is the total area of the field that needs to be fertilized? (Recall that the area of a rectangle is the product of the width and the length.)
10 years ago
RhondaSommer (rhondasommer):
\[\frac{\sqrt{3}\cdot \:50}{\sqrt{2}}\cdot \frac{\sqrt{5}\cdot \:80}{\sqrt{3}}\]
10 years ago
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RhondaSommer (rhondasommer):
\[\frac{\sqrt{3}\cdot \sqrt{5}\cdot \:50\cdot \:80}{\sqrt{2}\cdot \sqrt{3}}\]
10 years ago
RhondaSommer (rhondasommer):
\[\frac{\sqrt{5}\cdot \:50\cdot \:80}{\sqrt{2}}\]
10 years ago
RhondaSommer (rhondasommer):
\[\sqrt{5}\cdot \:4000\]
10 years ago
OpenStudy (imsleeziboii):
Huh? lol
10 years ago
RhondaSommer (rhondasommer):
\[\frac{4000\cdot \sqrt{5}}{\sqrt{2}}\]
10 years ago
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RhondaSommer (rhondasommer):
\[4000=2^5\cdot \:5^3\]
10 years ago
RhondaSommer (rhondasommer):
\[\frac{2^5\cdot \:5^3\cdot \sqrt{5}}{\sqrt{2}}\]
10 years ago
RhondaSommer (rhondasommer):
\[\frac{x^a}{x^b}\:=\:x^{a-b}\]\[\frac{2^5}{\sqrt{2}}=2^{5-\frac{1}{2}}=2^{\frac{9}{2}}\]
10 years ago
RhondaSommer (rhondasommer):
\[2^{\frac{9}{2}}\cdot \:5^{\frac{7}{2}}\]
10 years ago
RhondaSommer (rhondasommer):
im multiplying them by each other
10 years ago
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RhondaSommer (rhondasommer):
then i combined like terms
10 years ago
OpenStudy (imsleeziboii):
how you going so fast?
10 years ago
RhondaSommer (rhondasommer):
i did it on another paper XD
10 years ago
RhondaSommer (rhondasommer):
\[2^4\cdot \sqrt{2}\cdot \:5^{\frac{7}{2}}\]
10 years ago
RhondaSommer (rhondasommer):
\[2^4\cdot \sqrt{2}\cdot \:5^3\cdot \sqrt{5}\]
10 years ago
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OpenStudy (imsleeziboii):
Do you want the choices?
10 years ago
RhondaSommer (rhondasommer):
\[\sqrt{a}\sqrt{b}=\sqrt{ab}:\quad \sqrt{2}\cdot \sqrt{5}=\sqrt{2\cdot \:5}\] which equals \[2^4\cdot \:5^3\sqrt{2\cdot \:5}\]\[\sqrt{10}\cdot \:2000\]
10 years ago
RhondaSommer (rhondasommer):
there ya go
10 years ago
OpenStudy (imsleeziboii):
oh that is the answer lol ty
10 years ago
RhondaSommer (rhondasommer):
yeah
10 years ago