Square Root of 959

The square root is the inverse of squaring a number. 959 is not a perfect square. The square root of 959 is expressed in both radical and exponential form. In radical form, it is expressed as √959, whereas in exponential form it is (959^(1/2). √959 is approximately equal to 30.956, which is an irrational number because it cannot be expressed in the form of p/q, where p and q are integers and q ≠ 0.

The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers like 959, the long-division method and approximation method are used. Let us now learn the following methods: -

1. Prime factorization method 
2. Long division method 
3. Approximation method

The product of prime factors is the prime factorization of a number. Now let us look at how 959 is broken down into its prime factors:

Step 1: Finding the prime factors of 959 959 is not easily factorized into smaller primes, but it can be expressed as 7 x 137, where both 7 and 137 are primes.

Step 2: Since 959 is not a perfect square, the digits of the number cannot be grouped into pairs.

Therefore, calculating the square root of 959 using prime factorization alone is not feasible.

The long division method is particularly useful for non-perfect square numbers. In this method, we should check the closest perfect square number for the given number. Let us now learn how to find the square root using the long division method, step by step.

Step 1: To begin with, we need to group the numbers from right to left. In the case of 959, we need to group it as 59 and 9.

Step 2: Find n whose square is closest to 9. Here, n can be 3 because 3 x 3 = 9. Now the quotient is 3, and after subtracting 9-9, the remainder is 0.

Step 3: Bring down 59, which is the new dividend. Add the old divisor with itself: 3 + 3 = 6, which will be our new divisor.

Step 4: The new divisor will be 6n. Find the value of n such that 6n x n is less than or equal to 59. Let n be 9, as 69 x 9 = 621, which is too large. Try n = 8, giving 68 x 8 = 544.

Step 5: Subtract 544 from 590 (59 brought down after the initial group), leaving 46.

Step 6: Since the dividend is less than the divisor, we add a decimal point to our quotient and bring down two zeros to continue the long division. The new dividend is now 4600.

Step 7: Find the new divisor, which is 617, and find n such that 617n x n ≤ 4600. Trying n = 7, we get 617 x 7 = 4319.

Step 8: Subtracting 4319 from 4600 gives 281.

Step 9: Continue this process until the desired decimal accuracy is achieved.

So the square root of √959 is approximately 30.956.

The approximation method is another method for finding square roots and is an easy method to find the square root of a given number. Let us learn how to find the square root of 959 using the approximation method.

Step 1: Now we have to find the closest perfect square of √959. The smallest perfect square less than 959 is 900, and the largest perfect square more than 959 is 961. √959 falls somewhere between 30 and 31.

Step 2: Apply the approximation formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square).

For 959, (959 - 900) / (961 - 900) = 59 / 61 ≈ 0.967. Using the approximation, the square root is approximately 30 + 0.967 = 30.967.

• Square root: A square root is the inverse of squaring a number. Example: 4² = 16, and the inverse is the square root, √16 = 4.

• Irrational number: An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero, and p and q are integers.

• Prime factorization: Breaking down a number into its prime components. For example, the prime factorization of 28 is 2 x 2 x 7.

• Decimal: A number that has a whole number and a fractional part separated by a decimal point, such as 7.86 or 9.42.

• Approximation: Estimating a number to a nearby value for ease of calculation, often used in finding square roots of non-perfect squares.