Question

11664 square root by prime factorization





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Answer 1

Given:

$\sqrt{11664}$

To find:

The square root by Prime factorization

Solution:

To find the square root of 11664 by prime factorization, we will first find the factors by prime factorization method.

2 | 11664

   -----------

2 | 5832

  -----------

2 | 2916

   ----------

2 | 1458

   ----------

3 | 729

   ----------

3 | 243

   ----------

3 | 81

  -----------

3 | 27

  -----------

3 |  9

  ------------

3 |  3

  -------------

      1

  ---------------

∴ factors of 11664 = 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3 × 3 = 2⁴ × 3⁶

∴ Square Root of 11664 = $\sqrt{2^4 \times 3^6}$ = $\sqrt{2^2 \times2^2 \times3^2\times3^2\times3^2}$ = 2 × 2 × 3 × 3 × 3 = 108

Thus, the square root of 11664 is 108.

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Answer 2

The square root by prime factorization of 11664 is 108

Step-by-step explanation:

The prime factorization is determination of prime factors that are multiplied to form the number.

Now, we need to divide the numbers by prime numbers.

11,664 ÷ 2 = 5,832

5,832 ÷ 2 = 2,916

2,916 ÷ 2 = 1,458

1,458 ÷ 2 = 729

729 ÷ 3 = 243

243 ÷ 3 = 81

81 ÷ 3 = 27

27 ÷ 3 = 9

9 ÷ 3 = 3

3 ÷ 3 = 1

Now, the prime factors are:

2 × 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3 × 3 = 11664

2 × 2 × 3 × 3 × 3 = 108