Can you divide a square root by a negative?

Fractions with negative roots in the denominator or with i in the denominator must be rationalized (since i represents a square root). When dividing complex numbers with negative roots, simplify in terms of imaginary numbers and then multiply the numerator and denominator by i.

What is the rule for dividing negative exponents?

Dividing negative exponents is almost the same as multiplying them, except you’re doing the opposite: subtracting where you would have added and dividing where you would have multiplied. If the bases are the same, subtract the exponents. Remember to flip the exponent and make it positive, if needed.

What happens when you square a number with an even exponent?

We started with minus 3 and ended with plus 3. When we square a number, then take the square root, we may not end up with the number we started with! In fact we end up with the absolute value of the number: That also happens for all even (but not odd) Exponents. An even exponent always gives a positive (or 0) result.

Why are square roots both positive and negative?

Direct link to THE_ONE_AND_ONLY’s post “Square roots can be both because the factors are t…” Square roots can be both because the factors are the same number and same value, and also because positive*positive = positive squared and negative*negative = negative squared.

When does an exponent have a negative base?

And so you might notice a pattern here. Whenever we raised raised a negative base to an exponent, if we raise it to an odd exponent, we are going to get a negative value. And that’s because when you multiply negative numbers an even number of times, a negative number times a negative number is a positive.

Which is the correct way to divide square roots?

If we multiplied top and bottom by , we would get nowhere, as this would result: . Instead, let’s cross-multiply. Then, square both sides to get rid of the radical. Divide both sides by . The reason the negative is not an answer is because a negative value in a radical is an imaginary number. Rationalize the denominator: