Square Root of 4.84

The square root is the inverse of the square of the number. 4.84 is a perfect square. The square root of 4.84 is expressed in both radical and exponential form. In radical form, it is expressed as √4.84, whereas (4.84)^(1/2) in exponential form. √4.84 = 2.2, which is a rational number because it can 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, methods like long-division and approximation are also 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. Now, let us look at how 4.84 is broken down into its prime factors:

Step 1: Convert 4.84 to a fraction, which is 484/100.

Step 2: Find the prime factors of 484, which are 2 x 2 x 11 x 11: \(2^2 \times 11^2\).

Step 3: The prime factorization of 100 is 2 x 2 x 5 x 5: \(2^2 \times 5^2\).

Step 4: Take the square root of both numerator and denominator separately: √484/√100 = 22/10 = 2.2.

The long division method is particularly used for non-perfect square numbers. However, since 4.84 is a perfect square, we can also use it to verify the result.

Step 1: To begin with, we need to place 4.84 under the division symbol.

Step 2: Find a number whose square is less than or equal to 4. The number is 2, whose square is 4.

Step 3: Subtract 4 from 4, the remainder is 0. Bring down the next pair, which is 84.

Step 4: Double the quotient to get the new divisor, which is 4. Now, find a digit to place after this 4 so that the product is less than or equal to 84. The digit is 2 making it 42. 42 x 2 = 84.

Step 5: Subtract 84 from 84, the remainder is 0. So, the square root of √4.84 is 2.2.

The approximation method is another way to find square roots; it is useful for quick estimates. However, since 4.84 is a perfect square, we can use it to confirm the result.

Step 1: Identify two perfect squares between which 4.84 lies.

4 (2^2) and 9 (3^2) are perfect squares, and 4.84 lies between them.

Step 2: Since 4.84 is closer to 4, estimate that the square root is slightly more than 2.

Step 3: Calculate (4.84 - 4) / (9 - 4) to find a more precise estimate, which will indicate how much more than 2 the square root should be.

Step 4: Refine the estimate to 2.2, which is the exact square root of 4.84.

• Square root: A square root is the inverse operation of squaring a number. Example: 2.2² = 4.84 and the inverse operation is the square root, √4.84 = 2.2.

• Rational number: A rational number is a number that can be expressed in the form of p/q, where q is not equal to zero and p and q are integers.

• Perfect square: A number that is the square of an integer. Example: 4.84 is a perfect square because √4.84 = 2.2.

• Long division method: A technique to find the square root of a number by dividing it into smaller, more manageable parts.

• Decimal: A number that includes a whole number and a fractional part separated by a decimal point. Example: 2.2 is a decimal.