Square Root of 5.88

The square root is the inverse of the square of the number. 5.88 is not a perfect square. The square root of 5.88 is expressed in both radical and exponential form. In radical form, it is expressed as √5.88, whereas (5.88)^(1/2) in exponential form. √5.88 ≈ 2.425, 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, the prime factorization method is not practical for non-perfect square numbers where long-division and approximation methods are used. Let us now learn the following methods: 

• Prime factorization method 
• Long division method 
• Approximation method

The product of prime factors is the prime factorization of a number. However, since 5.88 is not a perfect square, it cannot be exactly decomposed into integer prime factors for calculating its square root. Therefore, calculating 5.88 using the prime factorization method is not feasible.

The long division method is particularly useful for non-perfect square numbers. Let us now learn how to find the square root using the long division method, step by step.

Step 1: Group the digits from the decimal point onwards. In the case of 5.88, treat it as 5.88 itself.

Step 2: Find a number (n) whose square is less than or equal to 5. The closest number is 2 since 2 × 2 = 4. Subtract 4 from 5, leaving a remainder of 1.

Step 3: Bring down the next two digits, 88, making it 188.

Step 4: Double the divisor from the previous step (2), giving us 4.

Step 5: Determine a digit (d) such that 4d × d is less than or equal to 188. The correct digit is 4, since 44 × 4 = 176.

Step 6: Subtract 176 from 188, leaving a remainder of 12.

Step 7: Bring down two more zeroes, making it 1200.

Step 8: Calculate the new divisor as 48 (4 doubled from the previous step) and find a digit d such that 48d × d is less than or equal to 1200. The correct digit is 2, since 482 × 2 = 964.

Step 9: Subtract 964 from 1200, leaving a remainder of 236.

Step 10: Repeat the process to refine the decimal further.

The square root of 5.88 is approximately 2.425.

The approximation method is another way to find square roots. It's a simple method to find the square root of a given number. Let us learn how to find the square root of 5.88 using the approximation method.

Step 1: Identify the closest perfect squares around 5.88.

The closest perfect squares are 4 and 9. √5.88 falls between 2 and 3.

Step 2: Apply the formula: (Given number - smaller perfect square) / (larger perfect square - smaller perfect square). Using the formula: (5.88 - 4) / (9 - 4) = 1.88 / 5 = 0.376

Step 3: Add this result to the smaller integer root approximation: 2 + 0.376 = 2.376.

However, further refinement gives a more precise approximation of 2.425 for √5.88.

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

• Irrational number: An irrational number is a number that cannot be written in the form of p/q where q ≠ 0 and p and q are integers.

• Principal square root: A number has both positive and negative square roots, but the principal square root is the positive one commonly used in real-world applications.

• Decimal: A decimal is a number that has a whole number and a fractional part, such as 7.86 or 8.65.

• Approximation method: A technique used to find a close estimate of a square root, especially useful for non-perfect squares.