Square Root of 4.8

The square root is the inverse of squaring a number. Since 4.8 is not a perfect square, its square root is expressed in both radical and exponential form. In radical form, it is expressed as √4.8, whereas in exponential form it is (4.8)^(1/2). √4.8 ≈ 2.19089, which is an irrational number because it cannot be expressed as a simple fraction.

For non-perfect square numbers, methods like the long division method and approximation method are used since the prime factorization method is not applicable. Let us now learn these methods:

• Long division method
• Approximation method

The long division method is useful for finding square roots of non-perfect square numbers. Here is how to find the square root of 4.8 using this method, step by step:

Step 1: First, we need to group the numbers from right to left. Since 4.8 is a single-digit decimal, we consider 4.8 as 48 with a decimal point later.

Step 2: Find a number (n) whose square is less than or equal to 4. We choose n as 2 because 2^2 = 4.

Step 3: Subtract 4 from 4, resulting in 0. Bring down 80, making the new dividend 80.

Step 4: Double the current quotient (2) to get 4, which will be the start of the new divisor.

Step 5: Find a digit (x) such that 4x * x is less than or equal to 80. Choose x as 2, because 42 * 2 = 84 is too large.

Step 6: Use 41 * 1 = 41. Subtract 41 from 80, resulting in 39.

Step 7: Since 39 is smaller than 41, we add a decimal point and bring down two zeroes, making the new dividend 3900.

Step 8: Double the current quotient (21) to get 42, which will be the first part of the new divisor.

Step 9: Find a digit (y) such that 42y * y is less than or equal to 3900. Choose y as 9, because 429 * 9 = 3861 is less than 3900.

Step 10: Subtract 3861 from 3900, resulting in 39. The quotient is 2.19.

The approximate value of √4.8 is 2.19.

The approximation method is a simpler way to find square roots. Here is how to find the square root of 4.8 using this method:

Step 1: Identify the closest perfect squares to 4.8.

The closest perfect squares are 4 (2^2) and 9 (3^2). Thus, √4.8 is between 2 and 3.

Step 2: Use linear interpolation to estimate the square root: (4.8 - 4) / (9 - 4) = 0.8 / 5 = 0.16 Add this to the lower bound: 2 + 0.16 = 2.16

Therefore, √4.8 is approximately 2.16.

• Square root: The square root of a number is a value that, when multiplied by itself, gives the original number. Example: √9 = 3.

• Irrational number: A number that cannot be written as a simple fraction (p/q where q ≠ 0) is called an irrational number. √4.8 is an example.

• Radical: A radical is an expression that includes a root, such as a square root or cube root. Example: √4.8.

• Decimal: A decimal is a number that consists of a whole number and a fractional part, separated by a decimal point. Example: 4.8.

• Approximation: The process of finding a value that is close to the exact answer, often used with irrational numbers. Example: √4.8 ≈ 2.19.