You may already know that a perfect square is a number whose square root is a whole number. You also know that every number has a square root, and most numbers are not perfect squares. If you need to find the square root of a number that is not a perfect square, you can determine which two whole numbers the root falls between.
Let’s look at an example.
Find 30−−√
First, you know that 30 is not a perfect square because there is no whole number you can multiply by itself to equal 30.
Next, you know the following perfect squares.
5×56×6==2536
The answer is 30−−√ is between 5 and 6.
Another way of approximating the square root is to use a calculator. All calculators have a radical sign on them. Some of them may work differently, but the procedure below should be similar.
Find 30−−√ using a calculator.
First, enter the number you would like to find the square root of, in this case, 30.
Next, enter the radical sign.
Then, press the equal sign.
The answer is 5.477225575
When you’re doing an estimate and writing it in an equation, it’s best to use the ≈ symbol, which means “approximately equal to.”
30−−√≈5.477225575
You can also round your answer to a decimal.
30−−√≈5.5
As you can see, 5.5 is between 5 and 6.
You can check the answer by squaring 5.5. Remember, this is an estimate that has also been rounded.
5.5×5.5=30.25
And 30.25≈30
Your calculator has a x2 key to help you square decimal numbers.
Estimate the value:
8.22
First, you know that 8 is the root of the perfect square 64.
Next, enter the number 8.2
Then hit the x2 key.
The answer is 67.24.
8.22=67.24
Since the answer on the calculator contains only two decimal places, this is an exact answer and does not require the ≈ sign.
Answers & Comments
Answer: Estimating Square Roots
You may already know that a perfect square is a number whose square root is a whole number. You also know that every number has a square root, and most numbers are not perfect squares. If you need to find the square root of a number that is not a perfect square, you can determine which two whole numbers the root falls between.
Let’s look at an example.
Find 30−−√
First, you know that 30 is not a perfect square because there is no whole number you can multiply by itself to equal 30.
Next, you know the following perfect squares.
5×56×6==2536
The answer is 30−−√ is between 5 and 6.
Another way of approximating the square root is to use a calculator. All calculators have a radical sign on them. Some of them may work differently, but the procedure below should be similar.
Find 30−−√ using a calculator.
First, enter the number you would like to find the square root of, in this case, 30.
Next, enter the radical sign.
Then, press the equal sign.
The answer is 5.477225575
When you’re doing an estimate and writing it in an equation, it’s best to use the ≈ symbol, which means “approximately equal to.”
30−−√≈5.477225575
You can also round your answer to a decimal.
30−−√≈5.5
As you can see, 5.5 is between 5 and 6.
You can check the answer by squaring 5.5. Remember, this is an estimate that has also been rounded.
5.5×5.5=30.25
And 30.25≈30
Your calculator has a x2 key to help you square decimal numbers.
Estimate the value:
8.22
First, you know that 8 is the root of the perfect square 64.
Next, enter the number 8.2
Then hit the x2 key.
The answer is 67.24.
8.22=67.24
Since the answer on the calculator contains only two decimal places, this is an exact answer and does not require the ≈ sign.
The answer is 67.24.
Explanation: