Sum of Power, Ex 1.1 Ch 1 Real Numbers Class 10 Maths NCERT New Syllabus #shorts #short #math #maths

EXERCISE 1.1
1. Express each number as a product of its prime factors:
(i) 140
(ii) 156
(iii) 3825
(iv) 5005
(v) 7429
2. Find the LCM and HCF of the following pairs of integers and verify that LCM × HCF = product of the two numbers.
(i) 26 and 91
(ii) 510 and 92
(iii) 336 and 54
3. Find the LCM and HCF of the following integers by applying the prime factorisation method.
(i) 12, 15 and 21
(ii) 17, 23 and 29
(iii) 8, 9 and 25
4. Given that HCF (306, 657) = 9, find LCM (306, 657).
5. Check whether 6^n can end with the digit 0 for any natural number n.
6. Explain why 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 are composite numbers.
7. There is a circular path around a sports field. Sonia takes 18 minutes to drive one round of the field, while Ravi takes 12 minutes for the same. Suppose they both start at the

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सिद्ध करो एक √2 अपरिमेय संख्या हैं Prove that √2 or √3 or √5 is a irrational number | Mann Ki Ganit
Theorem 1.4 : prove that √2 is irrational. Example 9 :
Prove that √3 is irrational.
EXERCISE 1.3
Q1. Prove that √5 is irrational.
प्रमेय 1.4 : सिद्ध कीजिए कि √2 अपरिमेय है। उदाहरण 9 :
सिद्ध कीजिए कि √3 अपरिमेय है।
व्यायाम 1.3
Q1. सिद्ध कीजिए कि √5 अपरिमेय है।
Example 10 : Show that 5– √3 is irrational.
Example 11 : Show that 3√2 is irrational.
Q2. Prove that 3 + 2√5 is irrational.
Q3. Prove that the following are irrationals : (i) 1 / √2 (ii) 7√5 (iii) 6 + √2
उदाहरण 10 : दर्शाइए कि 5- √3 अपरिमेय है।
उदाहरण 11 : दर्शाइए कि 3√2 अपरिमेय है।
प्रश्न २. सिद्ध कीजिए कि 3 + 2√5 अपरिमेय है।
Q3. सिद्ध कीजिए कि निम्नलिखित अपरिमेय हैं: (i) 1 / 2 (ii) 7√5 (iii) 6 + 2

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