Question

Find the smallest number by which 1440 must be divided to get a perfect square. Find the square root of the perfect square thus obtained.

pls in note step by step​

Answer 1

Answer:

Prime factorising 1440, we get,

1440=2×2×2×2×2×3×3×5

=2

5

×3

2

×5

1

.

We know, a perfect cube has multiples of 3 as powers of prime factors.

Here, number of 2's is 5, number of 3's is 2 and number of 5's is 1.

So we need to multiply another 2, 3 and 5

2

in the factorization to make 1440 a perfect cube.

Hence, the smallest number by which 1440 must be multiplied to obtain a perfect cube is 2×3×5

2

=150.

∴ The sum of digits of the smallest number is =1+5+0=6

Step-by-step explanation:

Prime factorising 1440, we get,

1440=2×2×2×2×2×3×3×5

=2

5

×3

2

×5

1

.

We know, a perfect cube has multiples of 3 as powers of prime factors.

Here, number of 2's is 5, number of 3's is 2 and number of 5's is 1.

So we need to multiply another 2, 3 and 5

2

in the factorization to make 1440 a perfect cube.

Hence, the smallest number by which 1440 must be multiplied to obtain a perfect cube is 2×3×5

2

=150.

∴ The sum of digits of the smallest number is =1+5+0=6.

Hence, option B is correct.

Answer 2

Step-by-step explanation:

Ist step

Take out the LCM of 1440

2×2×2×2×2×3×5×3×2

=2280

2nd step

Take out common factors

2×3×5×2

60

3rd step

2280-1440

=880

Hence must be added to 880 to 1440 to make perfect square