Square Root of 8.5

The square root is the inverse of the square of the number. 8.5 is not a perfect square. The square root of 8.5 is expressed in both radical and exponential form. In the radical form, it is expressed as √8.5, whereas (8.5)^(1/2) in the exponential form. √8.5 ≈ 2.91548, 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 typically used for perfect square numbers. However, for non-perfect square numbers like 8.5, the long division method and approximation method are preferred. Let us now learn these methods: Long division method Approximation method

The long division method is particularly used 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 8.5, consider the number as 8.50.

Step 2: Now, find n whose square is less than or equal to 8. The number n is 2 because 2 x 2 = 4, which is less than or equal to 8. Now the quotient is 2.

Step 3: Subtract 4 from 8, and bring down 50 to make it 450.

Step 4: Double the quotient (2), which is now 4. We need to find a number x such that 4x multiplied by x is less than or equal to 450.

Step 5: The next step is finding the value of x. Let us consider x as 9, then 49 x 9 = 441.

Step 6: Subtract 441 from 450; the difference is 9.

Step 7: Since the remainder is not zero, add two zeroes to continue the division.

Step 8: Continue the process to get two numbers after the decimal point.

The square root of 8.5 is approximately 2.91.

The approximation method is another method for finding square roots. It is an easy method to find the square root of a given number. Now let us learn how to find the square root of 8.5 using the approximation method.

Step 1: Find the closest perfect square of √8.5.

The closest perfect squares surrounding 8.5 are 4 and 9. √8.5 falls somewhere between 2 and 3.

Step 2: Now, apply the interpolation formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square)

Using the formula (8.5 - 4) / (9 - 4) = 0.9 Add the value we got initially to the base perfect square root, which is 2 + 0.9 = 2.9, so the square root of 8.5 is approximately 2.9.

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

• Irrational number: An irrational number cannot be expressed as a simple fraction, meaning it cannot be written as a ratio of two integers.

• Principal square root: This refers to the non-negative square root of a number. For example, the principal square root of 8.5 is approximately 2.915.

• Decimal: A decimal is a number that contains a whole number part and a fractional part separated by a decimal point. For example, 8.5 is a decimal.

• Approximation: This refers to a value or quantity that is nearly but not exactly correct; it is often used when calculating irrational numbers like square roots.