1. Prove that 3​ is an irrational number. 2. State fundamental theorem of..

The Fundamental Theorem of Arithmetic
The Fundamental Theorem of Arithmetic

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1. Prove that 3 is an irrational number. 2. State fundamental theorem

1. Prove that is an irrational number. 2. State fundamental theorem of Arithmetic and hence find the unique factorization of 120 . 3. Prove that is irrational 4. Prove that is an irrational number. 5. Find HCF and LCM of 56 and 112 by prime factorization method. 6. Explain why: (i) is a composite number (ii) is a composite number. (iii) is a composite number. 7. Find the largest number that divides 31 and 99 leaving remainder 5 and 8 respectively. 8. The HCF of 65 and 117 is expressible in the form . Find the value of . Also find the LCM of 65 and 117 using prime factorisation method. 9. Find the largest number that divides 1251, 9377 and 15628 leaving remainder 1,2 and 3 respectively. 10. Show that can never ends with unit digit zero. 11. HCF of and . 12. Find LCM\& HCF of 14 and 122 and verify the relation between them.

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Question Text

1. Prove that is an irrational number. 2. State fundamental theorem of Arithmetic and hence find the unique factorization of 120 . 3. Prove that is irrational 4. Prove that is an irrational number. 5. Find HCF and LCM of 56 and 112 by prime factorization method. 6. Explain why: (i) is a composite number (ii) is a composite number. (iii) is a composite number. 7. Find the largest number that divides 31 and 99 leaving remainder 5 and 8 respectively. 8. The HCF of 65 and 117 is expressible in the form . Find the value of . Also find the LCM of 65 and 117 using prime factorisation method. 9. Find the largest number that divides 1251, 9377 and 15628 leaving remainder 1,2 and 3 respectively. 10. Show that can never ends with unit digit zero. 11. HCF of and . 12. Find LCM\& HCF of 14 and 122 and verify the relation between them.

Updated On Feb 14, 2023
Topic All topics
Subject Mathematics
Class Class 9
Answer Type Video solution: 1
Upvotes 61
Avg. Video Duration 3 min

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