Square Root of 962

The square root is the inverse operation of squaring a number. The number 962 is not a perfect square. The square root of 962 is expressed in both radical and exponential form. In radical form, it is expressed as √962, whereas in exponential form it is written as 962^(1/2). The square root of 962 is approximately 31.014, which is an irrational number because it cannot be expressed as a fraction p/q, where p and q are integers and q ≠ 0.

The prime factorization method is typically used for perfect square numbers. However, for non-perfect squares like 962, the long division method and approximation method are more suitable. Let us explore these methods: -

1. Long division method 
2. Approximation method

The long division method is particularly useful for finding the square root of non-perfect square numbers. Here is how you can find the square root of 962 using the long division method, step by step:

Step 1: Begin by pairing the digits of 962 from right to left, which gives us 62 and 9.

Step 2: Find the largest number whose square is less than or equal to 9. That number is 3 because 3 × 3 = 9. Subtract 9 from 9, leaving a remainder of 0.

Step 3: Bring down the next pair, which is 62, making the new dividend 62.

Step 4: Double the divisor (3) to get 6, which becomes the new divisor prefix. Now, determine a digit n such that 6n × n is less than or equal to 62.

Step 5: The largest n satisfying this condition is 1, since 61 × 1 = 61. Subtract 61 from 62 to get a remainder of 1.

Step 6: Add a decimal point to the quotient and bring down two zeros to make the new dividend 100.

Step 7: Double the current quotient (31) to get 62. Find a digit n such that 62n × n is less than or equal to 100.

Step 8: The largest n is 1, since 621 × 1 = 621. Subtract 621 from 1000 to get a remainder of 379.

Step 9: Continue this process until you achieve the desired accuracy. The square root of 962 is approximately 31.014.

The approximation method provides a quick and easy way to estimate the square root of a number. Here's how to find the square root of 962 using this method:

Step 1: Identify the perfect squares nearest to 962. The perfect squares are 961 (31²) and 1024 (32²). Thus, √962 is between 31 and 32.

Step 2: Use the formula: (Given number - smaller perfect square) / (Larger perfect square - smaller perfect square). Using this formula: (962 - 961) / (1024 - 961) = 1/63 ≈ 0.0159.

Adding this to 31 gives approximately 31.0159, so √962 ≈ 31.014.

• Square root: The square root of a number is a value that, when multiplied by itself, gives the original number. Example: √16 = 4.

• Irrational number: A number that cannot be written as a simple fraction; its decimal form is non-repeating and non-terminating. Example: π, √2.

• Radical: The symbol (√) used to denote the root of a number. For example, √25 = 5.

• Approximation: A value or number that is close to but not exactly equal to another number; often used when dealing with irrational numbers.

• Long division method: A step-by-step process for dividing multi-digit numbers, often used to find square roots of non-perfect squares.