Square Root 1 to 20- Definition, Properties, Examples

Introduction: Square Roots

The square root of a number is a value that, when multiplied by itself, gives the original number. The concept of a square root dates back to ancient times and has been a cornerstone in mathematics and engineering. The symbol used to denote square root is . For instance, $9$ equals 3 because $3 \times 3$ is 9.

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Definition:

If $a^{2} = b$ , then $a$ is the square root of $b$ . Mathematically, it’s represented as $a = b$ .

Properties of Square Roots:

Product Property: The square root of a product is the product of the square roots. $ab = a \times b$
Quotient Property: The square root of a quotient is the quotient of the square roots. $b a = b a$
Positive Root: Every positive number has two square roots, one positive and one negative. However, the term “square root” usually refers to the positive root.
Zero: The square root of zero is zero.
Negative Numbers: The square roots of negative numbers are not real; they are complex numbers. For example, $-1$ is represented by the imaginary unit $i$ .
Perfect Squares: Numbers like 1, 4, 9, 16, etc., whose square roots are integers, are called perfect squares.

Square Roots from 1 to 20:

$1 = 1$
$2 \approx 1.414$
$3 \approx 1.732$
$4 = 2$
$5 \approx 2.236$
$6 \approx 2.449$
$7 \approx 2.646$
$8 \approx 2.828$
$9 = 3$
$10 \approx 3.162$
$11 \approx 3.317$
$12 \approx 3.464$
$13 \approx 3.606$
$14 \approx 3.742$
$15 \approx 3.873$
$16 = 4$
$17 \approx 4.123$
$18 \approx 4.243$
$19 \approx 4.359$
$20 \approx 4.472$

Examples:

Using the Product Property: $8 = 4 \times 2 = 4 \times 2 = 2 \times 1.414 \approx 2.828$
Using the Quotient Property: $4 9 = 4 9 = 2 3 = 1.5$

In conclusion, the concept of square roots is fundamental in mathematics, serving as a foundational topic in algebra, geometry, and even calculus. Its properties allow for simplifications and offer pathways to solve a wide range of problems. Whether you’re trying to determine the length of a side in a square or solving quadratic equations, the square root remains an indispensable tool in the mathematical toolkit.