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Question 1: Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion: Question 2: Write down the decimal expansions of those rational numbers in Question 1…
Read MoreQuestion 1: Prove that √5 is irrational. Question 2: Prove that 3 + √5 is irrational. Question 3: Prove that the following are irrationals:(i) 1/√2 (ii) 7√5 (iii) 6 + √2 Class 10 | Exercise 1.2 Class 10 | Exercise…
Read MoreQuestion 1: Express each number as a product of its prime factors: (i) 140 (ii) 156 (iii) 3825 (iv) 5005 (v) 7429 Question 2: Find the LCM and HCF of the following pairs of integers and verify that LCM ×…
Read MoreQuestion 1: Use Euclid’s division algorithm to find the HCF of :(i) 135 and 225 (ii) 196 and 38220 (iii) 867 and 255 Question 2: Show that any positive odd integer is of the form 6q+1, or 6q+3, or 6q+5,…
Read MoreExample 1 : Use Euclid’s algorithm to find the HCF of 4052 and 12576. Example 2: Show that every positive even integer is of the form 2q, and that every positive odd integer is of the form 2q + 1,…
Read MoreTheorem 1.1 (Euclid’s Division Lemma) : Given positive integers a and b, there exist unique integers q and r satisfying a = bq + r, 0 ≤ r < b. Euclid’s Division Algorithm : This algorithm is used to find…
Read MoreExample 18: Rationalise the denominator of 1/ (2 + √3) Example 19: Rationalise the denominator of 5 / (√3 – √5) Example 20: Rationalise the denominator of 1/ (7 + 3√2) Example 17 Example 21
Read MoreExample 16: Simplify the following expressions: (i) (5+ √7)(2+ √5) (ii) (5+ √5)(5− √5) (iii) (√3+ √7)2 (iv) (√11− √7)(√11+ √7) Example 12, 13, 14, 15 Example 17
Read MoreExample 12: Check whether 7 √5, 7/√5 , √2 +21, π − 2 are irrational numbers or not. Example 13: Add 2√2+5√3 and √2–3√3. Example 14: Multiply 6√5 by 2√5. Example 15: Divide 8√(15) by 2√3. Example 11 Example 16
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