Simplification
- The sum of the digits of the smallest number which, when multiplied by 1800, gives a perfect cube, is :
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1800 = 2 × 2 × 2 × 3 × 3 × 5 × 5 = 23 × 32 × 52
To make 1800 a perfect cube, it must be multiplied by 15 (least number).
∴ Required sum = 1 + 5 = 6Correct Option: C
1800 = 2 × 2 × 2 × 3 × 3 × 5 × 5 = 23 × 32 × 52
To make 1800 a perfect cube, it must be multiplied by 15 (least number).
∴ Required sum = 1 + 5 = 6
- Sum of digits of the smallest number by which 1440 be multiplied so that it becomes a perfect cube, is
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1440 = 2 × 2 × 2 × 2 × 2 × 3 × 3 × 5 = 23 × 22 × 32 × 5
To make 1440 a perfect cube, it must be mulitplied by 2 × 3 × 5 × 5 = 150.
∴ The required sum = 1+5 + 0 = 6Correct Option: B
1440 = 2 × 2 × 2 × 2 × 2 × 3 × 3 × 5 = 23 × 22 × 32 × 5
To make 1440 a perfect cube, it must be mulitplied by 2 × 3 × 5 × 5 = 150.
∴ The required sum = 1+5 + 0 = 6
- By which smallest number 1323 must be multiplied, so that it becomes a perfect cube?
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1323 = 3 × 3 × 3 × 7 × 7
∴ It must be multiplied by 7.Correct Option: D
1323 = 3 × 3 × 3 × 7 × 7
∴ It must be multiplied by 7.
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3√ 4 12 is equal to 125
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Expression = 3√ 4 12 125 = 3√ 512 = 3√ 8 × 8 × 8 125 5 × 5 × 5 = 8 = 1.6 5 Correct Option: B
Expression = 3√ 4 12 125 = 3√ 512 = 3√ 8 × 8 × 8 125 5 × 5 × 5 = 8 = 1.6 5
- The value of (√43 + 152)3 is
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Expression = (√43 + 152)3
= (√64 + 225)3 = (√289)3
= (17)3 = 4913Correct Option: A
Expression = (√43 + 152)3
= (√64 + 225)3 = (√289)3
= (17)3 = 4913
