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Which expression is equivalent to (first picture is the equation the rest are the answers)

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Which expression is equivalent to (first picture is the equation the rest are the-example-5

1 Answer

7 votes

The prime factorization of 108 is


108 = 2^2\cdot 3^3

This means that we have


√(-108) = √((-1)\cdot2^2\cdot 3^3) = √(-1)\cdot√(2^2)\cdot√(3^3) = √(-1)\cdot√(2^2)\cdot√(3^2\cdot 3) = √(-1)\cdot√(2^2)\cdot√(3^2)\cdot√(3)

We can simplify the squares and the square roots:


√(-1)\cdot√(2^2)\cdot√(3^2)\cdot√(3) = i\cdot 2\cdot 3 \cdot √(3) = 6i√(3)

Similarly, we have


√(-3) = √((-1)\cdot 3) = √(-1)\cdot√(3)=i√(3)

So, the difference is


√(-108)-√(-3) = 6i√(3)-i√(3) = 5i√(3)

User Jan Mares
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