Let's move on to see some square root examples, and learn how to find answers for square roots. You'll first have to keep in mind the steps to finding square roots and they are:
Estimate: Get as close as possible to the number you're trying to square root by finding two perfect square roots that gives a close number.
Divide: Divide your number by one of the square roots you've chosen from the previous step.
Average: Take the average of step 2 and the root.
Repeat: Keep repeating steps 2 and 3 using the results you got from step 3 until you get a number that's accurate enough for you to answer the question.
So in simpler words, to estimate square roots which are not perfect squares without using a calculator, we'll need to know the perfect square numbers well. We will first put the number inside the square root sign in the middle of a number line, and then find the two closest perfect square numbers on its left and right hand side to make the best estimation. Take a look at some of the below examples of square roots.
Square root of 5
Step 1: Estimate
The square numbers of 2 and 3 are 4 and 9 respectively. The number 5 lies between these two numbers.
Step 2: Divide
Divide 5 by either 2 or 3. In this case, let's choose 2. We'll get 2.5.
Step 3: Average
Average 2.5 and 2, which gives us 2.25.
Step 4: Repeat
To get a more accurate number, keep repeating step 2 and 3. In that case we'd take 5 and divide it by 2.25, which equals 2.222. Average out 2.22 and 2.25, giving us 2.235. You may repeat steps 2 and 3 as many times needed to get a more accurate number.
The final answer for the square root of 5 is approximately 2.23!
Square root of 8
Step 1: Estimate
8 lies between perfect squares of 2^2 and 3^2.
Step 2: Divide
Divide 8 by 3. We get 2.6666666
Step 3: Average
Average 2.6666666 and 3, which gives us 2.8333333
Step 4: Repeat
To get a more accurate number, keep repeating step 2 and 3.
You should get a final answer of 2.83.
Square root of 10
Step 1: Estimate
10 lies between perfect squares of 3^2 and 4^2.
Step 2: Divide
Divide 10 by 3. We get 3.33
Step 3: Average
Average 3.33 and 3, which gives us 3.1667
Step 4: Repeat
To get a more accurate number, keep repeating step 2 and 3.
You should get a final answer of 3.16.
Square root of 6
Step 1: Estimate
6 lies between perfect squares of 2^2 and 3^2.
Step 2: Divide
Divide 6 by 2. We get 3.
Step 3: Average
Average 3 and 2, which gives us 2.5
Step 4: Repeat
To get a more accurate number, keep repeating step 2 and 3.
You should get a final answer of 2.45.
Square root of 12
Step 1: Estimate
12 lies between perfect squares of 3^2 and 4^2.
Step 2: Divide
Divide 12 by 4. We get 3.
Step 3: Average
Average 3 and 4, which gives us 3.5.
Step 4: Repeat
To get a more accurate number, keep repeating step 2 and 3.
You should get a final answer of 3.46.
Square root of 20
Step 1: Estimate
20 lies between perfect squares of 4^2 and 5^2.
Step 2: Divide
Divide 20 by 5. We get 4.
Step 3: Average
Average 4 and 5, which gives us 4.5.
Step 4: Repeat
To get a more accurate number, keep repeating step 2 and 3.
You should get a final answer of 4.47.
Square root of 0
As a final note, we wanted to explore what the square root of 0 is. You can't take the square root of a negative number, but 0 is not a negative number. The square root of 0 is actually 0!
Answers & Comments
Answer:
How to find square roots without calculators
Let's move on to see some square root examples, and learn how to find answers for square roots. You'll first have to keep in mind the steps to finding square roots and they are:
Estimate: Get as close as possible to the number you're trying to square root by finding two perfect square roots that gives a close number.
Divide: Divide your number by one of the square roots you've chosen from the previous step.
Average: Take the average of step 2 and the root.
Repeat: Keep repeating steps 2 and 3 using the results you got from step 3 until you get a number that's accurate enough for you to answer the question.
So in simpler words, to estimate square roots which are not perfect squares without using a calculator, we'll need to know the perfect square numbers well. We will first put the number inside the square root sign in the middle of a number line, and then find the two closest perfect square numbers on its left and right hand side to make the best estimation. Take a look at some of the below examples of square roots.
Square root of 5
Step 1: Estimate
The square numbers of 2 and 3 are 4 and 9 respectively. The number 5 lies between these two numbers.
Step 2: Divide
Divide 5 by either 2 or 3. In this case, let's choose 2. We'll get 2.5.
Step 3: Average
Average 2.5 and 2, which gives us 2.25.
Step 4: Repeat
To get a more accurate number, keep repeating step 2 and 3. In that case we'd take 5 and divide it by 2.25, which equals 2.222. Average out 2.22 and 2.25, giving us 2.235. You may repeat steps 2 and 3 as many times needed to get a more accurate number.
The final answer for the square root of 5 is approximately 2.23!
Square root of 8
Step 1: Estimate
8 lies between perfect squares of 2^2 and 3^2.
Step 2: Divide
Divide 8 by 3. We get 2.6666666
Step 3: Average
Average 2.6666666 and 3, which gives us 2.8333333
Step 4: Repeat
To get a more accurate number, keep repeating step 2 and 3.
You should get a final answer of 2.83.
Square root of 10
Step 1: Estimate
10 lies between perfect squares of 3^2 and 4^2.
Step 2: Divide
Divide 10 by 3. We get 3.33
Step 3: Average
Average 3.33 and 3, which gives us 3.1667
Step 4: Repeat
To get a more accurate number, keep repeating step 2 and 3.
You should get a final answer of 3.16.
Square root of 6
Step 1: Estimate
6 lies between perfect squares of 2^2 and 3^2.
Step 2: Divide
Divide 6 by 2. We get 3.
Step 3: Average
Average 3 and 2, which gives us 2.5
Step 4: Repeat
To get a more accurate number, keep repeating step 2 and 3.
You should get a final answer of 2.45.
Square root of 12
Step 1: Estimate
12 lies between perfect squares of 3^2 and 4^2.
Step 2: Divide
Divide 12 by 4. We get 3.
Step 3: Average
Average 3 and 4, which gives us 3.5.
Step 4: Repeat
To get a more accurate number, keep repeating step 2 and 3.
You should get a final answer of 3.46.
Square root of 20
Step 1: Estimate
20 lies between perfect squares of 4^2 and 5^2.
Step 2: Divide
Divide 20 by 5. We get 4.
Step 3: Average
Average 4 and 5, which gives us 4.5.
Step 4: Repeat
To get a more accurate number, keep repeating step 2 and 3.
You should get a final answer of 4.47.
Square root of 0
As a final note, we wanted to explore what the square root of 0 is. You can't take the square root of a negative number, but 0 is not a negative number. The square root of 0 is actually 0!
Step-by-step explanation:
1. find the perfect square that is close to non-perfect square
(e.g the perfect square that is near to it was which results to 9, if you try you will exceed to 12 therefore it is between 3 and 4)
2. estimate (pick number between 3 and 4)
e.g =12.25 which is close to 12, so we can consider 3.5 as its approximate estimate for the