Question

Prime factarisation of a number is 2^5 x 3^6 x 7^2
Is this number a
perfect whe? find the least
number by which it should the multiplied, so
the resulting number is a perfect cube​

Answer 1

Answer:

Prime

factorisation of 2592=2×2×2×2×2×3×3×3×3

On grouping the factors in pairs, we notice that one 2 is left out. Hence,we should multiply 2592 with 2, so that prime factor 2 gets grouped in pairs.

Hence, 2592 should be multiplied by 2 to make it a perfect square.

Answer 2

Step-by-step explanation:

2⁵ × 3⁶ × 7²

We should know that, if a number is a perfect square, then all its prime factorization must have a power of 2 or multiples of 2 like 4,6,8,etc.

Similarly,

If a number is a perfect cube, then all its prime factorization must have a power of 3 or multiples of 3, like 6,9,12,etc.

So here the number is

2⁵ × 3⁶ × 7²

Here all the numbers do not have a power of 2 or multiples of 2 (look 2⁵.....)

So, it is not a perfect square

also, all the numbers dont have a power of 3 or multiple of 3 (look 2⁵ and 7².......)

So to make it a perfect cube we must make it a multiple of 3

so, 2⁵ × 2 = 2⁶

and, 7² × 7 = 7³

Thus,

(2⁵ × 3⁶ × 7²) should be multiplied by 2 and 7

so, the perfect cube will be

(2⁵ × 3⁶ × 7²) × 2 × 7

(2⁵ × 3⁶ × 7²) × 14

so, 14 must be multiplied to 2⁵ × 3⁶ × 7² to get a perfect

Hope it helped and you understood it........All the best