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Find the Smallest Number by Which the Following Number Must Be Multiplied to Obtain a Perfect Cube. 100 - Mathematics

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Question

Find the smallest number by which the following number must be multiplied to obtain a perfect cube.

100

Solution

100 = 2 × 2 × 5 × 5

Here, two 2s and two 5s are left which are not in a triplet. To make 100 a cube, we require one more 2 and one more 5.

Then, we obtain

100 × 2 × 5 = 2 × 2 × 2 × 5 × 5 × 5 = 1000 is a perfect cube

Hence, the smallest natural number by which 100 should be multiplied to make it a perfect cube is 2 × 5 = 10.

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APPEARS IN

 NCERT Solution for Mathematics Textbook for Class 8 (2018 (Latest))
Chapter 7: Cubes and Cube Roots
Ex. 7.1 | Q: 2.5 | Page no. 114
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Find the Smallest Number by Which the Following Number Must Be Multiplied to Obtain a Perfect Cube. 100 Concept: Cubes - Smallest Multiple that is a Perfect Cube.
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