Square root Least number Multiply & Divide

Example 1: Find the smallest number by which 180 must be multiplied so that the product becomes a perfect square. Solution: By Prime factorization method, we get By pairing the factors we get We notice 5 needs a pair so we multiply both sides by 5 180 = 2 x 2 x 3 x 3 x 5 180 x 5 = 2 x 2 x 3 x 3 x 5 x 5 Hence, the smallest number to be multiplied with 180 is 5. Incase of multiplication, multiply the number that needs a pair

Example 2: Find the smallest number by which 360 must be multiplied so that the product becomes a perfect square. Solution: By Prime factorization method, we get By pairing the factors we get We notice 2 and 5 need a pair so we multiply both sides by 2 x 5 360 = 2 x 2 x 2 x 3 x 3 x 5 360 x 2 x 5 = 2 x 2 x 2 x 2 x 3 x 3 x 5 x 5 Hence, the smallest number to be multiplied with 360 is 2 x 5 =10. Incase of multiplication, multiply the number that needs a pair

Example 3: Find the smallest number by which 1100 must be divided so that the quotient becomes a perfect square. Solution: By Prime factorization method, we get By pairing the factors we get We notice 11 is without pair so we divide both sides by 11 to remove it 1100 = 2 x 2 x 5 x 5 x 11 = 2 x 2 x 5 x 5 x 11 11 Hence, the smallest number to be divided with 1100 is 11. Incase of division, divide the number that is without a pair

Example 3: Find the smallest number by which 1152 must be divided so that the quotient becomes a perfect square. Solution: By Prime factorization method, we get By pairing the factors we get We notice 2 is without pair so we divide both sides by 2 to remove it 1152 = 2 × 2 × 2 × 2 × 2 x 2 x 2 x 3 x 3 = 2 × 2 × 2 × 2 × 2 x 2 x 2 x 3 x 3 2 Hence, the smallest number to be divided with 1152 is 2. Incase of division, divide the number that is without a pair

Try These: Find the smallest number by which 2880 must be multiplied so that the product becomes a perfect square. 2. Find the smallest number by which 1575 must be divided so that the quotient is a perfect square.