Square roots are useful in everyday life. No matter how hard they may be to grasp in school, you need to understand them because they have real-life applications. In this article, you will learn everything you need to know to be able to find square roots. By the time you finish reading, you will be your very own square root calculator, getting accurate results at the end of every equation.
What is a square root?
A square root is a number that, when multiplied by itself, will produce a specific quantity. Any pair of digits multiplied by each other can be a square root. The square root symbol is √.
Below are examples of square roots:
- The square root of 16 is 4 because 4 x 4 = 16
- The square root of 25 is 5 because 5 x 5 = 25
- The square root of 36 is 6 because 6 x6 = 36
What are square roots used for?
Once you know how to find the square root of numbers, you will realize that it has many applications in real life. Below are examples of square root use in everyday life.
Finance
The square root function is commonly used in finance. It is an essential tool to calculate the return rate of an investment that has matured or depreciated over a two-year period.
The square root formula to calculate the return rate is as follows:
R = √(V2 / V0) – 1
R= the return rate
V2= the ending value
V0= the starting value
Let’s now put some real numbers into this equation:
Mike invested $100 in Disney in 2020
Two years later, he sold his shares for $196
We now have a real-life scenario to input numbers into the formula. Therefore:
V2 = 196
V0 = 100
Therefore:
R = √(196 / 100) – 1
R = √(1.96) – 1
R = 1.4 – 1
R = 0.4
In this example, we see that a square number does not have to be a whole number. Decimal digits can also be square numbers.
Pythagorean Theorem
In addition to its uses in finance, square roots are also used in mathematical formulas, namely, Pythagoras’ Theorem. Pythagoras’ Theorem is an equation used to calculate the length of a side of a triangle. It is often used in construction and building work, in order to ensure that the correct measurements are used.
The theorem is used to derive the area of the hypotenuse of a right-angle triangle:
√(a2 + b2) = c
c = The hypotenuse
a = Side one
b = Side two
If you have a triangle with two sides that measure 6 feet and 8 feet respectively, and need to find the length of the longest side, you need to use the above formula as follows:
√(62 + 82) = c
√(36 + 64) = c
√(100) = c
10 = c
The length of the longest side is 10 feet. Always remember to include the correct unit. Otherwise, your answer will be wrong.
What is BODMAS in mathematics?
How to simplify a square root
When you have large multiple-digit numbers, you can simplify them to make them easier to work with. In order to simplify a square root, you need to be able to identify whether there are any perfect squares by finding factors for the number that you have.
Let’s take the example of √75
75 = 5 x 5 x 3
This is the equivalent of
5² x 3 = 75
Therefore,
√75 = √5² x 3
This is the same as
√75 = √5² x √3
This can be simplified further to
√75 = 5√3
The square root of a negative number
Most of the time, if you are being asked to calculate the square root of a number, it will be a positive number. The square root of a number can be either positive or negative because when you multiply a negative number by another negative number, it creates a positive number. If you were asked what the square root of 25 is, the answer could be either 5 or -5, as both of these numbers multiplied by themselves will give you the answer 25.
How to find the square root of a number
The subtraction method
If you have a perfect square, this is the easiest method to find the square root of a number. All you need to do is subtract odd numbers from the original number that you are trying to find the square root of, until you reach zero.
For example, if you were trying to find the square root of 25:
25 – 1 = 24
24 – 3 = 21
21 – 5 = 16
16 – 7 = 9
9 – 9 = 0
As it took you 5 attempts to get to the number 0, you can deduce that 5 is the square root of 25.
Estimation method
Estimating the answer to a mathematical question is the equivalent of making an educated guess based on the information you have on hand. In this case, you use the square numbers that you know, surround the number you are looking for, and work from there. This works well for any number whose square isn’t perfect.
Let’s try and find √15 with the estimation method. The closest perfect square pair of digits to 15 is √16 which is 4. But 16 is too big, so let’s square 3. This gives us 9, which we know is too small. We can deduce that the square of 15 lies somewhere between 3 and 4. Now, we need to find out whether the square of 15 is closer to 3 or 4. To do this, we need to square 3.5 and 4, which gives us the answers 12.25 and 16 respectively. As a result, we know that √15 must lie between 3.5 and 4, and is closer to 4.
You then need to use trial and error to find the exact square of 15. For example, you can take 3.8 squared and see that it equals 14.44. However, you know that it needs to be bigger than this. Therefore, you should check 3.9 squared, which comes to 15.21.
This is too big, Therefore, you need to try numbers that lie between 3.8 and 3.9. Eventually, you will discover that √15 = 3.872. This process is not recommended because of how long it takes, and since you are dealing with complicated decimal point numbers. It is easier to just do it on a calculator.
Long division method
The long-division algorithm is a more precise way to find answers for numbers that don’t have a perfect square. Let’s take 2,025 as an example. The first thing you need to do is break the number down into more manageable numbers. In this case, you would separate 20 and 25.
Next, you need to find the largest integer square of the leftmost number. In this case, that number is 20. The largest square integer of 20 is 4 as 4 x 4 = 16. Then, you take the square number 16 away from 20, which leaves us with 4.
You must jot down the number 4 and put the remaining 25 of the original number next to it, with the result that you have 425. While doing this, also write the number 4 to the far right of your current equation. You must now multiply that 4 by 2, which leaves you with 8. Make a note of the 8 under this equation.
You now need to fill in the equation 8 _ x _ =
In order to find the numbers you need, you need to calculate the largest possible square integer for the second of your original numbers, which is 25. This is a perfect square, and the answer is 5. You are then left with the following equation:
85 x 5 = 425
The two squares that you ended up with were 4 and 5, so your final square number and the answer to √2025 is 45.
How to solve a problem in mathematics?
How to find the square root on a calculator
The easiest way to find a square root is by using a calculator. Most calculators have a square root function built into them, which you can use without resorting to a square root formula. All you need to do is press the √ button, and then enter your original number into the calculator to get the answer. All you need to do is make sure you enter the correct digits.
Math tutoring services
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