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creativ13 [48]
3 years ago
12

a student's work to distribute and simplify a radical is shown below. Select the statement which best applies to the sample math

ematical 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. a. the student did not properly distribute the radicals b. the student overlooked combining one or more of the radical terms c. the student did not properly simplify all radicals d. the work shown above is correct
Mathematics
2 answers:
Sphinxa [80]3 years ago
7 0
(-5 \sqrt{20} + \sqrt{3} )(2+ \sqrt{3} )\\ \\ -10 \sqrt{20}-5 \sqrt{60}  +2 \sqrt{3}+ \sqrt{9}   \\  \\ -20 \sqrt{5}-10 \sqrt{15}+2 \sqrt{3}+3


Answer is <span>c. the student did not properly simplify all radicals.
[5</span>√60 = 10√15, not 20√15]
wel3 years ago
5 0

Answer:

C) The student did not properly simplify all radicals.

Step-by-step explanation:

We are given the following expression in the question:

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

We have to apply the distributive property.

Distributive Property:

  • The distributive property helps multiply a sum by multiplying each addend separately and then add the products.
  • (a+b)(c+d) = ac + ad + bc + bd

Applying the distributive property:

(-5\sqrt{20}+\sqrt{3})(2+\sqrt{3})\\(-5\sqrt{20})(2) + (-5\sqrt{20})(\sqrt3) + (\sqrt3)(2) + (\sqrt3)(\sqrt3)\\-10\sqrt{20}-5\sqrt{60}+2\sqrt3 +\sqrt9

This can be further simplified as:

-10\sqrt{20}-5\sqrt{60}+2\sqrt3+\sqrt9\\-20\sqrt{5}-10\sqrt{15}+2\sqrt3+3

The student simplified the radical as:

-40\sqrt{20}-20\sqrt{60}+2\sqrt3+\sqrt3

The student did a mistake in simplifying the radical. He did not solve the square roots properly.

C) The student did not properly simplify all radicals.

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