Question

Explain the error in Julie’s work in rewriting the radical expression.

Answer 1

The negative numbers do not have square roots. Therefore the question does not have a solution. That is where Julie made a mistake.

Explanation:

Answer 2

-6

Explanation:

First, let's take a look at this property:

`\displaystyle \large{ √(a) √(b) = √(ab) }`

This only works for a and b ≥ 0.

As for a & b < 0 which results in Imaginary Number, we have to convert in 'i' form.

We know that:-

`\displaystyle \large{ i = √( - 1) }`

Thus:

`\displaystyle \large{ √( - 3) \cdot √( - 12) = √(3) i \cdot √(12)i }`

Then we can multiply 12 & 3 in square root.

`\displaystyle \large{ √( - 3) \cdot √( - 12) = √(36) {i}^(2) }`

We know that:

`\displaystyle \large{ {i}^(2) = - 1}`

Convert i^2 to -1

`\displaystyle \large{ √( - 3) \cdot √( - 12) = √(36)( - 1) } \\ \displaystyle \large{ √( - 3) \cdot √( - 12) = - √(36)}`

Then evaluate √36 which is 6.

`\displaystyle \large{ √( - 3) \cdot √( - 12) = - 6}`

Therefore the answer should be -6.

Conclusion

Julie cannot use the √a√b = √ab property first because a & b both are < 0 and the property applies for a ≥ 0, b ≥ 0.