Describe how you would estimate the square root of a number that is not a perfect square without using a calculator.
The square root will be between the square root of the perfect squares just above and below the number.
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To estimate the square root of a number that is not a perfect square without using a calculator, you can follow these steps:
1. Choose two perfect square numbers that the given number falls between. For example, if you want to estimate the square root of 23, you can choose 16 and 25 as the perfect square numbers.
2. Find the difference between the given number and the lower perfect square number. In our example, the difference would be 23 - 16 = 7.
3. Divide the difference obtained in step 2 by the difference between the higher and lower perfect square numbers. In our example, the difference between 25 and 16 is 25 - 16 = 9, so we divide 7 by 9.
This division gives us a decimal value, which will be the fractional part of our estimated square root.
4. Take the square root of the lower perfect square number. In our example, the square root of 16 is 4.
5. Add the result from step 4 to the decimal value obtained in step 3. In our example, 4 + (7 / 9) = 4.77778 (rounded to five decimal places).
This estimated value of the square root (in our example, approximately 4.77778) is a close approximation of the actual square root of the given number. It's important to note that this method provides a rough estimate and may not be completely accurate.
The square root must be between the square roots of the perfect squares just above and just below your number.
The square root of 89 must be between 9 and 10.