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Mathematics 15 Online
OpenStudy (imsleeziboii):

Help

RhondaSommer (rhondasommer):

hi

OpenStudy (imsleeziboii):

hi

RhondaSommer (rhondasommer):

what u need help on?

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.)

RhondaSommer (rhondasommer):

\[\frac{\sqrt{3}\cdot \:50}{\sqrt{2}}\cdot \frac{\sqrt{5}\cdot \:80}{\sqrt{3}}\]

RhondaSommer (rhondasommer):

\[\frac{\sqrt{3}\cdot \sqrt{5}\cdot \:50\cdot \:80}{\sqrt{2}\cdot \sqrt{3}}\]

RhondaSommer (rhondasommer):

\[\frac{\sqrt{5}\cdot \:50\cdot \:80}{\sqrt{2}}\]

RhondaSommer (rhondasommer):

\[\sqrt{5}\cdot \:4000\]

OpenStudy (imsleeziboii):

Huh? lol

RhondaSommer (rhondasommer):

\[\frac{4000\cdot \sqrt{5}}{\sqrt{2}}\]

RhondaSommer (rhondasommer):

\[4000=2^5\cdot \:5^3\]

RhondaSommer (rhondasommer):

\[\frac{2^5\cdot \:5^3\cdot \sqrt{5}}{\sqrt{2}}\]

RhondaSommer (rhondasommer):

\[\frac{x^a}{x^b}\:=\:x^{a-b}\]\[\frac{2^5}{\sqrt{2}}=2^{5-\frac{1}{2}}=2^{\frac{9}{2}}\]

RhondaSommer (rhondasommer):

\[2^{\frac{9}{2}}\cdot \:5^{\frac{7}{2}}\]

RhondaSommer (rhondasommer):

im multiplying them by each other

RhondaSommer (rhondasommer):

then i combined like terms

OpenStudy (imsleeziboii):

how you going so fast?

RhondaSommer (rhondasommer):

i did it on another paper XD

RhondaSommer (rhondasommer):

\[2^4\cdot \sqrt{2}\cdot \:5^{\frac{7}{2}}\]

RhondaSommer (rhondasommer):

\[2^4\cdot \sqrt{2}\cdot \:5^3\cdot \sqrt{5}\]

OpenStudy (imsleeziboii):

Do you want the choices?

RhondaSommer (rhondasommer):

\[\sqrt{a}\sqrt{b}=\sqrt{ab}:\quad \sqrt{2}\cdot \sqrt{5}=\sqrt{2\cdot \:5}\] which equals \[2^4\cdot \:5^3\sqrt{2\cdot \:5}\]\[\sqrt{10}\cdot \:2000\]

RhondaSommer (rhondasommer):

there ya go

OpenStudy (imsleeziboii):

oh that is the answer lol ty

RhondaSommer (rhondasommer):

yeah

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