8√6 find the process
Answers
Your answer is 19.59
Answer:
HomeFree worksheetsFree lessonsGames & activitiesCurriculum guideReviews
How to calculate a square root without a calculator
and should your child learn how to do it
Most people in today's world feel that since calculators can find square roots, that children don't need to learn how to find square roots using any pencil-and-paper method. However, learning at least the "guess and check" method for finding the square root will actually help the students UNDERSTAND and remember the square root concept itself!
So even though your math book may totally dismiss the topic of finding square roots without a calculator, consider letting students learn and practice at least the "guess and check" method. Since it actually deals with the CONCEPT of square root, I would consider it as essential for students to learn.
Depending on the situation and the students, the "guess and check" method can either be performed with a simple calculator that doesn't have a square root button or with paper & pencil calculations.
Finding square roots by guess & check method
To find a decimal approximation to, say √2, first make an initial guess, then square the guess, and depending how close you got, improve your guess. Since this method involves squaring the guess (multiplying the number times itself), it uses the actual definition of square root, and so can be very helpful in teaching the concept of square root.
Example: what is square root of 20?
You can start out by noting that since √16 = 4 and √25 = 5, then √20 must be between 4 and 5.
Then make a guess for √20; let's say for example that it is 4.5. Square that, see if the result is over or under 20, and improve your guess based on that. Repeat this process until you have the desired accuracy (amount of decimals). It's that simple and can be a nice experiment for students!
Example: Find √6 to 4 decimal places
Since 22 = 4 and 32 = 9, we know that √6 is between 2 and 3. Let's guess (or estimate) that it is 2.5. Squaring that we get 2.52 = 6.25. That's too high, so we reduce our estimate a little. Let's try 2.4 next. To find the square root of 6 to four decimal places we need to repeat this process until we have five decimals, and then we will round the result.
Estimate Square of estimate High/low
2.4 5.76 Too low
2.45 6.0025 Too high but real close
2.449 5.997601 Too low
2.4495 6.00005025 Too high so the square root of 6 must be between 2.449 and 2.4495.
2.4493 5.99907049 Too low
2.4494 5.99956036 Too low, so the square root of 6 must be between 2.4494 and 2.4495
2.44945 5.9998053025 Too low, so the square root of 6 must be between 2.44945 and 2.4495.
This is enough iterations since we know now that √6 would be rounded to 2.4495 (and not to 2.4494).
Finding square roots using an algorithm
There is also an algorithm for square roots that resembles the long division algorithm, and it was taught in schools in days before calculators. See the example below to learn it. While learning this algorithm may not be necessary in today's world with calculators, working out some examples can be used as an exercise in basic operations for middle school students, and studying the logic behind it can be a good thinking exercise for high school students.
Example: Find √645 to one decimal place.
First group the numbers under the root in pairs from right to left, leaving either one or two digits on the left (6 in this case). For each pair of numbers you will get one digit in the square root.
To start, find a number whose square is less than or equal to the first pair or first number, and write it above the square root line (2):
2
√6 .45
Then continue this way:
2
√6 .45
- 4
2 45
2
√6 .45
- 4
(4 _) 2 45
2
√6 .45
- 4
(45) 2 45
Square the 2, giving 4, write that underneath the 6, and subtract. Bring down the next pair of digits. Then double the number above the square root symbol line (highlighted), and write it down in parenthesis with an empty line next to it as shown. Next think what
Step-by-step explanation:
please mark it as a brainliest answer it is my request to you please please please please please please please