Smallest number multiplied to get a perfect square

Transcript

Smallest number multiplied to get a perfect square Let’s do this by examples Question Finds the smallest number multiplied by 32 to get a perfect square. We see that, 32 = 2 × 2 × 2 × 2 × 2 Since 2 does not occur in pair, we multiply by 2 to make it a pair So, our number becomes 32 × 2 = 2 × 2 × 2 × 2 × 2 × 2 Now, it becomes a perfect square. So, we multiply 32 by 2 to make it a perfect square Question Finds the smallest number multiplied by 90 to get a perfect square. We see that, 90 = 2 × 3 × 3 × 5 Here, 2 & 5 do not occur in pairs So, we multiply by 2 and 5 to make pairs So, our number becomes 90 × 2 × 5 = 2 × 3 × 3 × 5 × 2 × 5 = 2 × 2 × 3 × 3 × 5 × 5 Now, it becomes a perfect square. So, we multiply 90 by 2 × 5 i.e. 10 to make it a perfect square Question Finds the smallest number multiplied by 120 to get a perfect square. We see that, 120 = 2 × 2 × 2 × 3 × 5 Here, 2, 3 & 5 do not occur in pairs So, we multiply by 2, 3 and 5 to make pairs So, our number becomes 120 × 2 × 3 × 5 = 2 × 2 × 2 × 3 × 5 × 2 × 3 × 5 = 2 × 2 × 2 × 2 × 3 × 3 × 5 × 5 Now, it becomes a perfect square. So, we multiply 120 by 2 × 3 × 5 i.e. 30 to make it a perfect square