Hence 1 will be the power of our radicand. Meanwhile, the numerator of the fractional exponent is 1. This means that the index of our radical is 3. Solution: The denominator of the fractional exponent is 3. Therefore, a 3/4 is equal to ∜a 3.Įxample 5: Write (y – 1) ⅓ as a radical expression. Hence, it will be the power of our radicand. Meanwhile, the numerator of the fractional exponent is 3. This means that the index of our radical is 4. Solution: The denominator of the fractional exponent of a 3/4 is 4. Thus, √15 = 15 1/2.Įxample 4: Write a 3/4 as a radical expression. Solution: The index of √15 is 2 and we have 1 as the power of the radicand. Since we don’t have to write 2 as an index, the answer is √j.Įxample 1: Write √ 15 as an expression with fractional exponents. Thus, the index or degree of the radical of √16 is 2.Įxample: Determine the radicand and index of the following radical expressions: A missing index in the radical implies the square root of a number. If the index is missing, it means that the index is equal to 2. If the index is 4, it means we are taking the 4th root if the index is 5, it means we are taking the 5th root, and so on.īut what if the index is missing like in the case of √16? In the case of ∛x, we are taking the cube root since the index is 3. The index also tells us what root we are taking. For instance, in ∛x, the index or degree is 3. This number tells us how many times we should multiply the resulting number to obtain the radicand. This is the tiny number that you can see on the upper left side of the radical sign. Lastly, we have the index or degree of the radical. In ∛x, the radicand is x since it is the quantity inside the radical sign. It is the one that you are taking the root of.
On the other hand, the radicand is the quantity inside the radical sign. This means that we are taking the cube root of the number inside the radical sign. In this case, we are seeing the radical symbol with a 3 written on the left side. The radical symbol or radical sign is the symbol that indicates we are taking the root of a number.
We can extend the concept of square roots and cube roots to the fourth root (∜), fifth root, sixth root, and so on. For instance, ∛27 = 3 since 3 x 3 x 3 = 27. The cube root of the number is the number that when you multiplied to itself thrice (or three times) will produce the original number. However, radicals are not just square roots. You know that the square root of a number is the number that when multiplied by itself will produce the original number. The first time you probably encountered radicals is when you first learned about the square root of numbers. 2. Answer Key What Is a Radical?Ī radical is an expression or quantity that has the radical symbol or uses a root (√).
What Does “Rationalize the Denominator” Mean?.Rationalizing the Denominator of a Radical Expression.Radicals As Quantities With Fractional Exponents.In particular, we’ll study quantities raised to the power of a fraction, also known as radical expressions.
This time, we are going to explore the realm of quantities with exponents that are rational numbers. In the previous chapters, you encountered quantities with exponents that are integers (i.e., 0, positive whole numbers, and negative whole numbers).