Question

What is the smallest number by which you have to multiply the product 9 x 10 x 5 x 11 x 15 to get a perfect cube number?

Answer 1

Step-by-step explanation:

just find the prime factors of the given number(s) and if the all prime factors occur in a group of 3, then it's already a prefect , and if they don't, then just multiply the remaining prime factors needed to make a group of 3. Like it's done in the answer above, 2 and 11 were already there, just needed two 2s and two 11s more to make a group of 3.

And you can skip the ³√ part. directly right the factors

Answer 2

Given :- What is the smallest number by which you have to multiply the product 9 x 10 x 5 x 11 x 15 to get a perfect cube number ?

Answer :-

checking the factors we get,

→ N = 9 * 10 * 5 * 11 * 15

→ N = 3 * 3 * 2 * 5 * 5 * 11 * 3 * 5

→ N = 3 * 3 * 3 * 5 * 5 * 5 * 2 * 11

→ N = 3³ * 5³ * 2 * 11

now, in order to be a perfect cube , all prime numbers must have a power of 3 .

then,

→ N = 3³ * 5³ * 2 * 2² * 11 * 11²

therefore,

→ N = 3² * 5³ * 2 * 11 * (4 * 121)

→ N = 3² * 5³ * 2 * 11 * 484

hence, we have to multiply the given product by 484 to get a perfect cube number.

Learn more :-

वह छोटी से छोटी संख्या बताईये जिसमे 7,9,11 से भाग देने पर 1,2,3 शेष बचे

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