Question

find the square root of 3024 by prime factorisation​

Answer 1

We have:

3024

We have to find, the square root of 3024 by prime factorization.​

Solution:

3024 = 2 × 1512

= 2 × 2 × 756

= 2 × 2 × 2 × 378

= 2 × 2 × 2 × 2 × 189

= 2 × 2 × 2 × 2 × 3 × 63

= 2 × 2 × 2 × 2 × 3 × 3 × 21

= 2 × 2 × 2 × 2 × 3 × 3 × 3 × 7

$\therefore$ $\sqrt{3024 }$ = 2 × 2 × 3 × $\sqrt{3\times 7}$

= 12$\sqrt{21}$

Hence, the square root of 3024 by prime factorization is 12$\sqrt{21}$.

Answer 2

Given : 3024

To Find : square root of 3024 by prime factorisation​

Solution:

3024 = 2 * 1512

= 2 * 2 * 756

= 2 * 2 * 2 * 378

= 2 * 2 * 2 * 2 * 189

= 2 * 2 * 2 * 2 * 3 * 63

= 2 * 2 * 2 * 2 * 3 * 3 * 21

= 2 * 2 * 2 * 2 * 3 * 3 * 3 * 7

= 2² * 2² * 3² * 21

√3024 = 2 * 2 * 3 √21

= 12√21

≈ 55

if it was 3025

then 3025  = 5 * 5  * 11 *  11

= 5² * 11²

√3025 = 5 * 11 = 55

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