Learning Objectives:

Some numbers are called **Perfect Squares**. It is important we can recognize **Perfect Square** when working with **Square Roots**.

To determine the **Square Root** of a number we use a special symbol i.e. . The **Square Root** of a number is the number times itself that equals the given number.

We can think of the **Square Root** as the opposite or **Inverse of Squaring**. Actually, numbers have two Square Roots. One is positive and another is negative.

*The Pythagorean Theorem:*

In a Right Triangle, the Square of the hypotenuse is equal to the sum of the Squares of the other two sides called legs. i.e. **.**

The proof is based on the proportionality of two similar triangles, that is, upon the fact that the ratio of any two corresponding sides of similar triangles is the same regardless of the size of the triangles.

*The Distance Formula:*

The distance between the two points and is given as –

This is a result of the **Pythagorean Theorem**.

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**Hook Questions:**

*1. **What is Square Root of a number? How is it stated?*

*2. **State and prove Pythagorean Theorem.*

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