How to find square root of decimal numbers without calculator

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  • SQUARE ROOT OF DECIMALS WITHOUT CALCULATOR

    Square root of a number is the factor that we multiply by itself two times to get that number.

    To find square root of decimals, we have two different ways,

    • Using prime factorization
    • Using long division

    To use prime factorization, we will convert the decimal as integer by multiplying it by 10n.

    Find :

    Problem 1:

    √0.01

    Solution :

    = √0.01

    After the decimal, we have two digits.

    So multiply the numerator and denominator by 100.

    = √1/100

    = √1/√100

    = 1/10

    = 0.1

    Problem 2 :

    √0.25

    Solution :

    = √0.25

    After the decimal, we have two digits. So multiply the numerator and denominator by 100.

    = √(25/100)

    = √25/√100

    = √(5⋅5)/√(10⋅10)

    = 5/10

    = 0.5

    Problem 3 :

    √0.81

    Solution :

    = √0.81

    = √81/100

    = √81/√100

    = √(9⋅9)/√(10⋅10)

    = 9/10

    = 0.9

    Problem 4 :

    √0.6889

    Solution :

    = √0.6889

    = √6889/10000

    = √6889/√10000

    Since the unit digit is 9 and starts with 68.

    83 x 83 = 6889

    87 x 87 = 7569

    = 83/100

    = 0.83

    Problem 5 :

    √0.7921

    Solution :

    = √0.7921

    = √7921/10000

    = √7921/√10000

    Since the unit digit is 1 and start

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