A **radical** is mathematical way to represent fractional exponents. A *radical* consists of a **radical sign**, a quantity under the radical sign called the **radicand**, and the **index** of the radical.

If an expression, let’s say *a*, is raised to the power of ½, that’s the same as taking the **square root** (√) of a (see below). Finding the square root of a number means (also known as *second root*) suggests that you’re looking for a number, that when multiplied in itself twice, gives you the radicand.

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What’s the

square root(orsecond root) of the number 4? Can you think of a number, when multiplied in itself twice, gives you 4? If you thought of ±2, you’re right! Given that the answer is an integer, 4 is called aperfect square. null

Similarly, if *a* is raised to ⅓, that’s the same as taking the **cube root** (∛) – also known as the *3 ^{rd} root*. Now you’re looking for a number, when multiplied in itself 3 times, gives you the radicand.

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What’s the

cube root(orthird root) of the number 27? Can you think of a number, when multiplied in itself 3 times, gives you 27? If you thought of ±3, you’re right! Given that the answer is an integer, 27 is called aperfect cube. null

Notice how an index of 2 **isn’t** displayed with the root symbol because it is automatically assumed to be a second root. Furthermore, if the numerator of the fractional exponent has a number other than 1, the numerator acts as the exponent to the *radicand*. This relationship is shown below:

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Question:Evaluate the expression show below: null

Solution:First we change the expression to radical form: nullIt becomes apparent that you need to evaluate what’s within the parentheses first – the cube root of 8 is 2. Raising 2⁵ is equal to

32. null

You will need to know how to convert between radical expressions and fractional exponents. The video below shows a few examples:

Another learning expectation is that you know how to simplify algebraic expressions containing fraction exponents without the aid of your calculator. Four examples pertaining to this are shown below:

- Still need more?
**Part 2**can be accessed here.