Question

find the square root of 7056 by prime factorization method

Answer 1

Answer:

$\sqrt{7056}=84$

Step-by-step explanation:

Resolve 7056 into product of prime, we get

2| 7056

_______

2| 3528

_______

2| 1764

_______

2| 882

_______

3| 441

_______

3| 147

_______

7| 49

_______

*** 7

7056 = 2×2×2×2×3×3×7×7

$\sqrt{7056}=\sqrt{2^{4}\times 3^{2}\times 7^{2}}\\=2^{2}\times 3 \times 7\\=84$

Therefore,

$\sqrt{7056}=84$

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Answer 2

Answer:

$2 |7056 \\ 2 |3528 \\ 2 |1764 \\2 |884 \\ 3 |441 \\ 3 |147 \\ 7 |49 \\ 7 |7 \\ 1 \\ 7056 = 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times | 7 \times 7 \\ \sqrt{7056 = 2 \times 2 \times 3 \times 3 \\ = 84}$