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To find the square root (वर्गमूल) of the fraction (882)/(1922).

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Answer

2131\frac{21}{31}

Step-by-step solution

3 steps
  1. Understand the problem.

    The problem asks to find the square root (वर्गमूल) of the fraction 8821922\frac{882}{1922}.

  2. Simplify the fraction 8821922\frac{882}{1922} first.

    Find the prime factorization of the numerator, 882:

    882=2×441882 = 2 \times 441 441=21×21=32×72441 = 21 \times 21 = 3^2 \times 7^2

    So, 882=2×32×72882 = 2 \times 3^2 \times 7^2.

    Find the prime factorization of the denominator, 1922:

    1922=2×9611922 = 2 \times 961 961=31×31=312961 = 31 \times 31 = 31^2

    So, 1922=2×3121922 = 2 \times 31^2.

    Divide both the numerator and the denominator by their greatest common divisor (GCD), which is 2:

    8821922=882÷21922÷2=441961\frac{882}{1922} = \frac{882 \div 2}{1922 \div 2} = \frac{441}{961}
  3. Find the square root of the simplified fraction.

    441961\sqrt{\frac{441}{961}}

    This can be written as the square root of the numerator divided by the square root of the denominator:

    441961\frac{\sqrt{441}}{\sqrt{961}}

    Calculate the square root of the numerator:

    441=212=21\sqrt{441} = \sqrt{21^2} = 21

    Calculate the square root of the denominator:

    961=312=31\sqrt{961} = \sqrt{31^2} = 31

    Substitute these values back into the expression:

    2131\frac{21}{31}

    The square root of 8821922\frac{882}{1922} is 2131\boxed{\frac{21}{31}}.

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