The square root of a number is a value that, when multiplied by itself, gives the original number. In other words, it is the value that, when squared, equals the given number. The square root of 8 can be written as √8 or 8^(1/2).
The square root of 8 is approximately 2.828
Step 1: Start with a guess for the square root. In this case, let's start with 2.
Step 2: Divide the number, 8, by the guess. 8 divided by 2 is 4.
Step 3: Average the guess and the result from the division. (2 + 4) / 2 = 3.
Step 4: Repeat steps 2 and 3 using the new guess. Divide 8 by 3 to get 2.67. Average 3 and 2.67 to get 2.83.
Step 5: Repeat steps 2 and 3 again. Divide 8 by 2.83 to get 2.82. Average 2.83 and 2.82 to get 2.828.
Step 6: Keep repeating steps 2 and 3 until you reach the desired level of accuracy. In this case, 2.828 is a good approximation for the square root of 8.
Therefore, the square root of 8 is approximately 2.828.
The square root of 8 is an irrational number. An irrational number is a number that cannot be expressed as a fraction of two integers. The decimal representation of the square root of 8 is non-terminating and non-repeating, indicating its irrationality.
Q: How can I convert a fraction to a decimal? A: To convert a fraction to a decimal, divide the numerator by the denominator. For example, to convert 3/4 to a decimal, divide 3 by 4, which gives 0.75.
Q: Can the square root of a negative number be real? A: No, the square root of a negative number is not a real number. It is an imaginary number. The square root of -1 is denoted as "i" in mathematics.
Q: What is the difference between a rational and an irrational number? A: A rational number is a number that can be expressed as a fraction of two integers, while an irrational number cannot be expressed as a fraction and has a non-terminating and non-repeating decimal representation.
Q: Can the square root of a perfect square be irrational? A: No, the square root of a perfect square is always a rational number. A perfect square is a number that can be expressed as the square of an integer.
Q: How can I estimate the square root of a number? A: One way to estimate the square root of a number is to find the two perfect squares that the number lies between and take the average of their square roots. For example, to estimate the square root of 10, we can find that it lies between the perfect squares 9 and 16. The square root of 9 is 3, and the square root of 16 is 4. Taking the average of 3 and 4 gives an estimate of 3.5.