Describe how you would estimate the square root of a number that is not a perfect square without using a calculator.
Can someone please explain? I need some help.
Find the perfect square just below and just above your number.
For instance, if your number is 85, the perfect squares above and below it must be 100 and 81. The square root of 85 is between 9 and 10.
I'm sorry I don't really understand... :(
that was like years ago bro
To estimate the square root of a number that is not a perfect square without using a calculator, you can use a process called the "Babylonian method" or the "Newton-Raphson method." Here's a step-by-step explanation of how to do it:
Step 1: Choose an initial guess for the square root. This can be any number you think might be close to the actual square root. It's helpful to pick a number that is easy to work with.
Step 2: Divide the number for which you are finding the square root by your initial guess. This will give you a quotient.
Step 3: Average the quotient from Step 2 with your initial guess. This will give you a new guess.
Step 4: Repeat Steps 2 and 3 several times, with each iteration using the previous guess to calculate a new quotient and average it with the previous guess. The more iterations you do, the closer your estimate will be to the actual square root.
Step 5: Continue repeating the process until you reach a satisfactory level of accuracy. You can determine this by comparing your estimates to the actual square root or by the level of precision you desire.
By following these steps, you will gradually converge on a more accurate estimate of the square root, even if the number is not a perfect square. However, note that this method is an approximation and your final estimate may still have some degree of error.