Question

find the square root of following numbers by prime factorization method (1) 576 (2)5625 (3) 441​

Answer 1

Answer:

576 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3

576 = 2 × 2 × 2 × 3

576 = 24

5625 = 3 × 3 × 5 × 5 × 5 × 5

5625 = 3 × 5 × 5

5625 = 75

441 = = 3 × 3 × 7 × 7

441 = 3 × 7

441 = 21

Step-by-step explanation:

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Answer 2

$(1) \: 576$

$= 8 \times 8 \times 3 \times 3 \\ = 8 \times 3 \times 8 \times 3$

$24 \times 24$

$= {24}^{2}$

$(2) \: 5625$

$=9 \times 25 \times 25 \\ = 3 \times 3 \times 5 \times 5 \times 5 \times 5$

$=3 \times 5 \times 5\times 3 \times 5 \times 5$

$=75 \times 75$

${75}^{2}$

$(3) \: 441$

$=7 \times 7 \times 3 \times 3 \\ = 7 \times 3 \times 7 \times 3$

$=21 \times 21$

${21}^{2}$