Learning Objectives:

__Math Tutoring on Introduction to Radical Expressions__

**Perfect squares** are the numbers that we obtain when we square an integer. So here we see the integers from** 1** through **10**, and if we square them, we get perfect squares, for example,** 0² = 0, 1² = 1, 2² = 4, 3² = 9, 4² = 16, 5² = 25, 6² = 36, 7² = 49, 8² = 64, 9² = 81 and 10² = 100.** To determine the **square root** of a number we have a special symbol as we see here, **√9 = 3**, **square root** of **9** is **3**. The **square root** of a number is a number times itself that equals the given number. Actually, numbers have two **square roots**, one positive and one negative, **+3•+3 = 9** and **-3•-3 = 9.** Let’s take a look at a definition of nth roots. If we let **a **and **b** be real numbers and **n** be an integer **> or = 2.** If we have an equation in the form of **a = bᵑ,** then** b** is an **n**th root of **a.** If **n = 2** the root is a **square** **root**, if **n = 3** the root is a **cube root**, if **n = 4** we have a **4**th root and so on. Inverse properties of nth powers and nth roots are as follows:

When **n** is odd , when **n** is even .

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**Hook Questions:**

*1. What is the nth root of a number? *

*2. What is the inverse of the power function? *

*3. How do you find the square root of a power?*

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