Question 10 Cube and Cube Roots Exercise 4.1 Next
Answer:
(i) 675 First find the factors of 675 675 = 3 × 3 × 3 × 5 × 5 = 33 × 52 ∴To make a perfect cube we need to multiply the product by 5. (ii) 1323 First find the factors of 1323 1323 = 3 × 3 × 3 × 7 × 7 = 33 × 72 ∴To make a perfect cube we need to multiply the product by 7. (iii) 2560 First find the factors of 2560 2560 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 5 = 23 × 23 × 23 × 5 ∴To make a perfect cube we need to multiply the product by 5 × 5 = 25. (iv) 7803 First find the factors of 7803 7803 = 3 × 3 × 3 × 17 × 17 = 33 × 172 ∴To make a perfect cube we need to multiply the product by 17. (v) 107811 First find the factors of 107811 107811 = 3 × 3 × 3 × 3 × 11 × 11 × 11 = 33 × 3 × 113 ∴To make a perfect cube we need to multiply the product by 3 × 3 = 9. (vi) 35721 First find the factors of 35721 35721 = 3 × 3 × 3 × 3 × 3 × 3 × 7 × 7 = 33 × 33 × 72 ∴To make a perfect cube we need to multiply the product by 7.
Was This helpful? Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts Dedicated counsellor for each student Detailed Performance Evaluation view all coursesOpen in App Suggest Corrections 5 On factorising 7803 into prime factors, we get: \[7803 = 3 \times 3 \times 3 \times 17 \times 17\] On grouping the factors in triples of equal factors, we get: \[7803 = \left\{ 3 \times 3 \times 3 \right\} \times 17 \times 17\] It is evident that the prime factors of 7803 cannot be grouped into triples of equal factors such that no factor is left over. Therefore, 7803 is a not perfect cube. However, if the number is multiplied by 17, the factors can be grouped into triples of equal factors such that no factor is left over. |