help me understand how to solve this problem. thanks
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A square root can be broken up like this:
√a*b = √a √b
Using this property, √-18 can be written as √-1 √18. But √-1 is defined as i, so you have i√18.
√18 can be further simplified by using the same property as above:
√9*2 = √9 √2 = 3√2.
So far we have i * √18 = i * 3√2. Write them more neatly to get 3i√2. The negative sign outside your original square root turns this to -3i√2.
√a*b = √a √b
Using this property, √-18 can be written as √-1 √18. But √-1 is defined as i, so you have i√18.
√18 can be further simplified by using the same property as above:
√9*2 = √9 √2 = 3√2.
So far we have i * √18 = i * 3√2. Write them more neatly to get 3i√2. The negative sign outside your original square root turns this to -3i√2.