Smallest number divided to get a Perfect Cube

Transcript

Smallest number divided to get a Perfect Cube Let’s do this by examples Question Finds the smallest number divided to 1125 to get a perfect cube We see that, 1125 = 3 × 3 × 5 × 5 × 5 Since 3 does not occur triplets, we divide by 3 × 3 to make a triplet So, our number becomes 1125 × 𝟏/𝟑 × 𝟏/𝟑 = 3 × 3 × 5 × 5 × 5 × 𝟏/𝟑 × 𝟏/𝟑 = 5 × 5 × 5 Now, it becomes a perfect cube. So, we divide 1125 by 3 × 3 i.e. 9 to make it a perfect cube Question Finds the smallest number divided to 5324 to get a perfect cube. We see that, 5324 = 2 × 2 × 11 × 11 × 11 Here, 2 does not occur in triplets So, we divide by 2 × 2 to make triplet So, our number becomes 5324 × 𝟏/𝟐 × 𝟏/𝟐 = 2 × 2 × 11 × 11 × 11 × 𝟏/𝟐 × 𝟏/𝟐 = 11 × 11 × 11 Now, it becomes a perfect cube. So, we divide 5324 by 2 × 2 i.e. 4 to make it a perfect cube Question Finds the smallest number divided to 968 to get a perfect cube. We see that, 968 = 2 × 2 × 2 × 11 × 11 Here, 11 does not occur in triplets So, we divide by 11 × 11 to make triplet So, our number becomes 400 × 𝟏/𝟐 × 𝟏/𝟓 × 𝟏/𝟓 = 2 × 2 × 2 × 2 × 5 × 5 × 𝟏/𝟐 × 𝟏/𝟓 × 𝟏/𝟓 = 2 × 2 × 2 Now, it becomes a perfect cube. So, we divide 400 by 2 × 5 × 5 i.e. 50 to make it a perfect cube