Question

Find the smallest number by which 256 and 72 must be multiplies to get a perfect square...plzz answer fast... thankyou

Answer 1

Answer:

«Prime factors of 256 = (2 × 2 × 2) ×( 2 × 2 × 2) × 2 × 2

Here, two 2s are left which are not in a triplet. To make 256 a cube, one more 2 is required. so, we multiply 256 by 2 to make it a perfect cube

256 × 2 = (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2) = 512 is a perfect cube.

Hence, the smallest natural number by which 256 should be multiplied to make it a perfect cube is 2.

«Prime factors of 72 = (2 × 2 × 2) × 3 × 3

Here, two 3s are left which are not in a triplet. To make 72 a cube, one more 3 is required. so, we multiply 72 by 3 to make it a perfect cube.

72 × 3 = (2 × 2 × 2) × (3 × 3 × 3) = 216 is a perfect cube.

Hence, the smallest natural number by which 72 should be multiplied to make it a perfect cube is 3.

Answer 2

16^2=256

72=3x3x2x2x2

now group them.

we find that one 2 is left out.

therefore 72 shoul be multiplied by 2to make it a perfect square

72x2=144 (which is a perfect square