Question

Simplify: 10 √3-√12-3√6

A.) 8√3-3√6
B.)10√3-√3-√6
C.)√12
D.) None of the above

Answer 1

Answer: Choice A

`8√(3)-3√(6)`

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Work Shown:

`\text{x} = 10√(3)-√(12)-3√(6)\\\\\text{x} = 10√(3)-√(4*3)-3√(6)\\\\\text{x} = 10√(3)-√(4)*√(3)-3√(6)\\\\\text{x} = 10√(3)-2√(3)-3√(6)\\\\\text{x} = (10√(3)-2√(3))-3√(6)\\\\\text{x} = (10-2)√(3)-3√(6)\\\\\text{x} = 8√(3)-3√(6)\\\\`

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Therefore,

`10√(3)-√(12)-3√(6)\\ \ \text{simplifies to} \\ 8√(3)-3√(6)\\\\`

In other words we can say

`10√(3)-√(12)-3√(6)=8√(3)-3√(6)\\\\`

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Verification:

Use a calculator to compute the following.

`10√(3)-√(12)-3√(6) \approx 6.507937\\\\8√(3)-3√(6) \approx 6.507937\\\\`

Since we get the same approximate decimal value, it helps us confirm the answer is correct.