Question

find the square root of 144 by prime factors station method
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Answer 1

Answer:

12

Step-by-step explanation:

1 2 × 1 2 = 144

12 is the squre root of 144

Answer 2

To find : square root of $144$ by prime factorization method .

Solution :

• As per the data given in the question, we have to find the square root of $144$  by prime factorization method .
• There are four methods to find square root of numbers :

1. Repeated subtraction method of square root
2. Square root by prime factorization method
3. Square root by estimation method
4. Square root by long division method.

• Finding square root of $144$ by prime factorization method:

• Prime factors of $144 = 2\times 2\times 2\times 2\times 3\times 3$

                                         $= 2^{4}\times 3^{2}$

• Taking one common factor from each pair.

      $\sqrt{144}= 2^{2}\times 2^{2}\times 3^{2} \\\sqrt{144} = \sqrt{((2\times 2\times 3)^{2} } \\\sqrt{144} = ((2\times 2\times 3)^{2} )^{\frac{1}{2} }$  

    $\sqrt{144} =$ ± $( 2\times 2\times 3)$

     $\sqrt{144} =$ ± $12$  

Hence, the square root of $144$ by prime factorization method is ± $12$  .