chellossav
Answered

A student's work to distribute and simplify a radical is shown below. Select the statement which best applies to the sample mathematical work.given (-5√20+√3)*(2+√3), i first distribute to get the expression -10√20-5√60+2√3+√9, which i can simplify to -40√5-20√15+2√3+3 for an answer.Which simplifies to 10 as the answer?

AThe student did not properly distribute the radicals.
BThe student did not properly combine the radicals.
CThe student did not properly simplify the radical at the end.
DThe work shown above is correct.

Verified Answer :

(-5\(\sqrt{20}\) + \(\sqrt{3}\)) * (2 + \(\sqrt{3}\)) = 
-10\(\sqrt{20}\) - 5\(\sqrt{60}\) +2\(\sqrt{3}\) + \(\sqrt{9}\) = 

\(\sqrt{20} = \sqrt{ 2^{2}*5 } = 2 \sqrt{5}\) 

\(\sqrt{60} = \sqrt{ 2^{2} * 3 * 5 } = 2 \sqrt{15}\)

The problem is the student square root wrongly

The final results is:

-20\(\sqrt{5}\) - 10\(\sqrt{15}\) + \(2 \sqrt{3}\) +3

The right answer for the question above is: 
C. C. The student did not properly simplify the radical at the end.

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