Real Numbers — Flashcards
Tamil Nadu Board · Class 9 · Mathematics
25 flashcards for Real Numbers (Tamil Nadu Board Class 9 Mathematics) to test yourself on key terms and facts.
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Find any two rational numbers between 1/2 and 2/3.
Answer
Step 1: Use the formula (p+r)/(q+s) where p/q = 1/2 and r/s = 2/3. Step 2: First rational number = (1+2)/(2+3) = 3/5 Step 3: Find another between 1/2 and 3/5 = (1+3)/(2+5) = 4/7 Verification: 1/2 = 0.
Convert the decimal 2.945 into the form p/q where p and q are integers and q ≠ 0.
Answer
Step 1: Write 2.945 = 2 + 0.945 Step 2: 0.945 = 945/1000 (move decimal 3 places) Step 3: Convert to mixed number: 2.945 = 2 + 945/1000 = (2 × 1000 + 945)/1000 = 2945/1000 Step 4: Simplify by finding G…
Convert 0.35̄ (where 5 repeats) into p/q form.
Answer
Step 1: Let x = 0.3555... Step 2: Multiply by 10: 10x = 3.555... Step 3: Multiply by 100: 100x = 35.555... Step 4: Subtract equation 2 from equation 3: 100x - 10x = 35.555... - 3.555... Step 5: 90x = …
Classify these numbers as rational or irrational: (i) √10 (ii) √49 (iii) 0.025 (iv) 0.76̄
Answer
Step 1: √10 - Check if 10 is a perfect square. It's not (3² = 9, 4² = 16). √10 is IRRATIONAL Step 2: √49 - This equals 7 = 7/1, which is RATIONAL (49 is a perfect square) Step 3: 0.025 - This is a ter…
Express √8 in simplest form (as a pure surd).
Answer
Step 1: Factor 8 = 4 × 2 = 2² × 2 Step 2: √8 = √(4 × 2) Step 3: √8 = √4 × √2 (using law of radicals) Step 4: √8 = 2√2 Answer: 2√2 Verification: (2√2)² = 4 × 2 = 8 ✓ Note: Pure surd has coefficient 1, …
Express ∛192 in simplest form.
Answer
Step 1: Factor 192 = 64 × 3 = 4³ × 3 Step 2: ∛192 = ∛(64 × 3) Step 3: ∛192 = ∛64 × ∛3 (using law of radicals) Step 4: ∛192 = 4∛3 Verification: (4∛3)³ = 4³ × 3 = 64 × 3 = 192 ✓ Answer: 4∛3 Order of sur…
Add: 3√7 + 5√7. Is the answer rational or irrational?
Answer
Step 1: Identify like surds - both have √7 (same radicand) Step 2: Apply addition rule: a√b + c√b = (a + c)√b Step 3: 3√7 + 5√7 = (3 + 5)√7 Step 4: = 8√7 Answer: 8√7 (IRRATIONAL) Explanation: When we …
Simplify: √63 - √175 + √28
Answer
Step 1: Simplify each surd separately √63 = √(9 × 7) = 3√7 √175 = √(25 × 7) = 5√7 √28 = √(4 × 7) = 2√7 Step 2: All have same radicand (7), so they are like surds Step 3: Combine: 3√7 - 5√7 + …
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