Square root in mathematics
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The document provides an introduction to square roots, detailing their mathematical definition and importance. It explains how to find square roots through factorization and includes examples for both whole numbers and fractions, as well as exercises. Additionally, it addresses word problems involving square roots, demonstrating practical applications.
Square root in mathematics
- 1. Nazish Jamali BS Education Batch-16
- 2. Square Root
- 3. Introduction • A number that produces a specified number when it is multiplies by itself. OR Square root of a number is a value that, when multiplied by itself, gives the number.
- 4. Examples i. 4 x 4 = 16, 4 is called the square root of 16. ii. (−4) × (−4) = 16, so −4 is also a square root of 16.
- 5. • This means every number has two square roots, one is positive another one is negative, but the square root of number is always positive. • called the radical. • For example: √36 = 6 , (because 6 x 6 =36
- 6. • "Squared" is often written as a little 2 like this: This says "4 Squared equals 16"
- 8. square root by Factorization 01. √256 = √2x2x2x2x2x2x2x2 = 2x2x2x2 = 16 Verification: 16 x 16 = 256 2 256 2 128 2 64 2 32 2 16 2 8 2 4 2 2 1
- 9. Exercise 4.1 12. √2025 = √3x3x3x3x5x5 = 3x3x5 =45 3 2025 3 675 3 225 3 75 5 25 5 5 1
- 10. Square root of common fractions The following rule is to be remembered for obtaining the square root of a common fraction. Square root of fraction = square root of numerator / square root of denominator If p and q be two natural numbers, then the square root of P²/q² is expressed as, √ P²/q² = √ P² / √ q² = √pxp / √qxq = p/q
- 11. Example Find the square root of 64/81 Sol: √64/81 = √64/ √81 = √8x8 / √9x9 = 8/9
- 12. Square root of Decimal friction We first convert it into a common fraction and then find the square root by the method of finding the square root of common fractions. The result obtained changed into decimal fraction.
- 13. Example 1. Find the square root of 1.44 Sol: √1.44 = √144 / 100 = √3x3x2x2x2x2 / 5x5x2x2 = √3²x2²x2² / 5²x2² = 3x2x2 / 5x2 = 12/10 = 1.2
- 14. Word Problems on square root Example: The area of a square park is 169 sq.m. what is the length of a side of the park? Sol: Length of the area = √Area of the square park = √169 = √13x13 =13m
- 15. Thank You