May 26, 2024

# 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 3×3 is 9.

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Definition:

If �2=�, then is the square root of . Mathematically, it’s represented as �=�.

Properties of Square Roots:

1. Product Property: The square root of a product is the product of the square roots. ��=�×�
2. Quotient Property: The square root of a quotient is the quotient of the square roots. ��=��
3. 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.
4. Zero: The square root of zero is zero.
5. Negative Numbers: The square roots of negative numbers are not real; they are complex numbers. For example, −1 is represented by the imaginary unit .
6. 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=1
2. 2≈1.414
3. 3≈1.732
4. 4=2
5. 5≈2.236
6. 6≈2.449
7. 7≈2.646
8. 8≈2.828
9. 9=3
10. 10≈3.162
11. 11≈3.317
12. 12≈3.464
13. 13≈3.606
14. 14≈3.742
15. 15≈3.873
16. 16=4
17. 17≈4.123
18. 18≈4.243
19. 19≈4.359
20. 20≈4.472

Examples:

1. Using the Product Property: 8=4×2=4×2=2×1.414≈2.828
2. Using the Quotient Property: 94=94=32=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.

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