Question

Q.5 Find the smallest number by which 1280 must be divided to get a perfectcube Also, find the cube root of the perfect cube so obtained.
step by step explaination for brainliest​

Answer 1

Answer:

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Step-by-step explanation:

1280÷20=64, it is the perfect cube of 4.

Answer 2

Solution :-

Finding the prime factors of 1280 we get,

→ 1280 = (2 * 2 * 2) * (2 * 2 * 2) * 2 * 2 * 5

now, we know that, for a number to be perfect cube , all prime factors must be in pair of three . But as we can see that, (2 * 2 * 5) are not in pair of three .

therefore, we can conclude that, the smallest number by which 1280 must be divided to get a perfect cube is multiple of 2 * 2 * 5 .

→ 2 * 2 * 5 = 20 (Ans.)

now, cube root of number so obtained will be,

→ 2 * 2 { taking one number from each pair } = 4 (Ans.)

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