Show how 3/4 × 4 can be solved using repeated addition.
2 answers:
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The original can be rewritten as 
. Because i^2 is equal to -1, we can replace the -1 in each radicand with i^2, like this: 
. Now, i-squared is a perfect square that can be pulled out of each radicand as a single i. 
. 24 has a perfect square hidden in it. 4 * 6 = 24 and 4 is a perfect square. So let's break this up, step by step. 
and then 
. We will now multiply the i and the 2i, and multiply the square root of 6 times the square root of 6: 
. 36 itself is a perfect square because 6 * 6 = 36. So we will do that simplification now. 
. Multiplying the 2 and the 6 gives us 
. But here we are back to the fact that i-squared is equal to -1, so 2(-1)(6) = -12. See how that works?