how to get the square root of a non-perfect square?
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how to get the square root of a non-perfect square?
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Steps in Finding/Calculating the Square Root of a Non-Perfect Square:
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Answer:
we need to find the prime factors of the perfect square. The perfect square is factorized into its prime factors by successive division. The pairs of the prime factors are paired. Taking the product of one factor from each pair will result in the square root of the perfect square.
Let us find the square root of 441. The prime factorization of 441 is 441 = 3 × 3 × 7 × 7. Pairing the prime factors and selecting one from each pair gives 3 × 7 = 21. So, the square root of 441 = √441 = 21.Let us find the square root of 180. The prime factorization of 180 is 180 = 2 × 2 × 3 × 3 × 5. If we make the pair of the prime factors we see that the prime factor 5 is not in the pair. Therefore 180 is not a perfect square and hence the square root is not perfect. The square root of 180, √180 = 2 × 3 × √5 = 6√5.Division Method
Calculating a square root for a large number by prime factorization method often time-consuming. To overcome this, we use the division method to find the square root of a large number. Steps for calculating square root by division method for perfect squares
Take the number whose square root is to find.Place a bar over every pair of the digit of the number starting from that in unit’s place (rightmost side).We divide the leftmost number by the largest number whose square is less than or equal to the number under the leftmost bar.Take this number as the divisor and the quotient. The number under the leftmost bar is considered to be the dividend.Divide and get the remainder.Bring down the number under the next bar to the right of the remainder.Double the divisor (or add divisor to itself).To the right of this divisor find a suitable number which together with divisor forms a new divisor for the new dividend. The new number in the quotient will have the same number as selected in the divisor. The condition is the same as being either less or equal to that of the dividend.
This process continues till we get zero as the remainder. The quotient thus obtained will be the square root of the number.
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