Distribute the referral code to your friends and ask them to register with Tutorix using this referral code. Once we get 15 subscriptions with your referral code, we will activate your 1 year subscription absolutely free. Your subscribed friend will also get 1 month subscription absolutely free. Uh-Oh! That’s all you get for now. We would love to personalise your learning journey. Sign Up to explore more. Sign Up or Login Skip for now Uh-Oh! That’s all you get for now. We would love to personalise your learning journey. Sign Up to explore more. Sign Up or Login Skip for now On factorising 8192 into prime factors, we get: \[8192 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2\] On grouping the factors in triples of equal factors, we get:
\[8192 = \left\{ 2 \times 2 \times 2 \right\} \times \left\{ 2 \times 2 \times 2 \right\} \times \left\{ 2 \times 2 \times 2 \right\} \times \left\{ 2 \times 2 \times 2 \right\} \times 2\] It is evident that the prime factors of 8192 cannot be grouped into triples of equal factors such that no factor is left over. Therefore, 8192 is not a perfect cube. However, if the number is divided by 2, the factors can be grouped into triples of equal factors such that no factor is left over.Hence, the number 8192 should be divided by 2 to make it a perfect cube. Also, the quotient is given as: \[\frac{8192}{2} = \frac{\left\{ 2 \times 2 \times 2 \right\} \times \left\{ 2 \times 2 \times 2 \right\} \times \left\{ 2 \times 2 \times 2 \right\} \times \left\{ 2 \times 2 \times 2 \right\} \times 2}{2}\] To get the cube root of the quotient 4096, take one factor from each triple. We get:
Hence, the required numbers are 2 and 16.
Question 7 Cube and Cube Roots Exercise 4.3 Next
Answer:
The prime factors of 8192 are 8192 = 2×2×2×2×2×2×2×2×2×2×2 = 23 ×23 ×23 ×2 Since, one triples remain incomplete, hence 8192 is not a perfect cube. So, we divide 8192 by 2 to make its quotient a perfect cube. 8192/2 = 4096 4096 = 2×2×2×2×2×2×2×2×2×2×2×2 = 23 ×23 ×23 ×23 Cube root of 4096 = ∛4096 = ∛ (23 ×23 ×23 ×23 ) = 2×2×2×2 = 16
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Calculation: 8192 = (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2) × 2 ∴ 8192 should be divided by 2 to make the resulting number a perfect cube. 8192/2 = 4096 4096 is a 16. The correct option is 4 i.e. 2 A perfect cube is a number that is equal to the number, multiplied by itself, three times. India’s #1 Learning Platform Start Complete Exam Preparation
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