In mathematics, we use exponents as a way to abbreviate repeated multiplication.

Example:

The exponent form of 6 x 6 is 6^{2}. There are two parts to exponent notation:

(1) the base which is the number 6

(2) the exponent which is the small elevated number 2

The base tells you what number is being multiplied and the exponent tells you how many times this number is used as a factor. In the above example the base is 6 and the exponent is 2.

**Square**

When the exponent is 2 the result is called the square. Recall that 6^{2} means 6 x 6. That is, 6 appears as a factor two times. The base is the variable 6. You also have an **x ^{2}** button on your calculator to speed up squaring. Locate it on your calculator and use it to solve the questions in the practice problems.

**Square roots**

We say that 2 is a square root of 4 because 2 x 2 = 4. What is interesting about the numbers 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, . . . ? Do you recognize them? These numbers are the squares or second powers of the counting numbers,1, 2, 3, 4, 5, 6, 7, 8, 9, 10, . . . :

^{2 }= 1

^{2 }= 4

^{2 }= 9

^{2 }= 16

^{2 }= 25, and so on. 1, 4, 9, 16, 25, . . . are called perfect squares.

Ancient Greek mathematicians called certain numbers square numbers or perfect squares because they could be represented by a square array of dots.

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The number of dots along the side of the square was called the root or origin of the square number. We call it the square root. When you square this number, or multiply it by itself, you obtain the original number.

Example

(a) The square root of 16 is 4, because 4^{2} or 4×4 = 16

(b) The square root of 64 is equal to 8 because 8^{2} or 8×8 = 64

**Square Root**

The sign √ is used to indicate the square root

**Finding the Square root**

How do you find the square root of any number? Using a calculator is the easiest way. Find out where the √ button is on your calculator and whether it is a second function **2ndF** or not. Find it and use it to figure out the practice problems.

Get a $20-or-so dual-display scientific calculator, even if you can`t take it with you into the exam hall. A calculator is also a learning tool, Technology Use is one of the 9 Essential Skills you can`t do without. Trying out different functions on a calculator will further your understanding and help with building a bigger mental picture. It builds links between numbers and algebra. It is important to try alternative calculations or approaches, to sketch & label angles, tracking changes to units of measure, visualizing to cross-link the concepts of area and numbers.