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Doha

PPT On Surds

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Published in: GMAT | Mathematics | Maths
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Grade 10 "Surds" with solved examples and practice questions

Saima J / Doha

4 years of teaching experience

Qualification: Master of Science in Materials Engineering

Teaches: Chemical, Maths, Chemistry, Physics, Science, Advanced Maths, Science Projects

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  1. Understanding Surds Grade 10 Mathematics
  2. What Are Surds? • •A surd is an irrational number that cannot be simplified to remove the square root (or other roots). • • Examples: 112, 1/3, V5 • • Non-examples: i./4 = 2, '19 = 3 (these are rational numbers).
  3. Why Study Surds? • • Surds appear in geometry, trigonometry, and real-world applications. • • Helps in understanding irrational numbers and their properties. • • Provides a foundation for higher mathematics.
  4. Properties of Surds • Va + 11b = i/(a + b) (Va)A2 = a • Surds remain irrational unless simplified to a perfect square.
  5. Simplifying Surds • Break the number under the root into its factors. • Example: = x 2) = 5v2 • Factorize to identify perfect squares.
  6. Rationalizing the Denominator • • Eliminate surds from the denominator by multiplying numerator and denominator by the conjugate. • • Example: 1/112 (1/\/2) x 612/112) = 112/2.
  7. Operations with Surds • Addition: 112 + 112 = 2112 • Subtraction: 31/3 - 1/3 = 2\/3 • Multiplication: •vi2 x 1/3 = • Division: 1,16 +1/3 = 112.
  8. Geometrical Connection • • Diagonal of a square: If side = a, diagonal = 112 x a. • • Example: For a square with side 1, diagonal = 112.
  9. Surds in Geometry (Note: Diagram placeholder, image not found)
  10. Real-life Examples • Architecture: Diagonal measurements. • Physics: Wave mechanics and energy calculations. • Engineering: Stress and strain ratios.
  11. Practice Questions • 1. Simplify: 1172 • 2. Rationalize: 5/1/3 • 3. Add: + • 4. Multiply: 117 n/14 • 5. Subtract: 61/2 - 4x/2.
  12. Answers • 2. 5\/3/3 • 4. 1/98 =
  13. Recap • • Surds are irrational roots. • • Can be simplified or rationalized. • • Appear in geometry, real-life, and advanced math.

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