Square root is one of the important knowledge in mathematics that is used throughout the learning process of students. The article below will introduce to you what the definition of square root is, and how to calculate the square root of a number? Please refer.
What is square root?
The square root of a number a is a number x such that x2 = a, or in other words, a number x squared = a.
For example, 2 and −2 are square roots of 2 because 2² = (−2)² = 4.
The radical sign is denoted by √
- Every non-negative real number a has a unique non-negative square root, called the arithmetic square root.
For example: The arithmetic square root of 16 is 4, symbol √16 = 4, because 4² = 4 × 4 = 16 and 4 is a non-negative number.
Every positive number a has two square roots: √a is a positive square root and −√a is a negative square root. They are denoted together as ± √a.
The most basic square root calculations
Remember some of the most basic and common square numbers so that when calculating square roots, you can mentally calculate faster:
0² = 0
1² = 1
3² = 9
4² = 16
5² = 25
6² = 36
7² = 49
8² = 64
9² = 81
10² = 100
11² = 121
12² = 144
13² = 169
14² = 196
15² = 225
16² = 256
17² = 289
Some basic square root formulas that everyone must remember include:
Square root table
The square root table is divided into rows and columns, allowing direct finding of square roots of numbers greater than 1 and less than 100.
Square roots of numbers written with no more than three digits from 1.00 to 99.9 are recorded in the table in columns 0 to 9. Next are nine correction columns used to correct letters. The last digit of the square root of the four-digit numbers from 1,000 to 99.99.
Example 1: Find
→ Solution:
At the intersection of rows 1,4 and column 1 we see the number 1,187
So
Example 2:
Find
At the intersection of rows 2,3 and column 5 we see the number 1,533. I have
Next, at the intersection of rows 2,3 and column 4 correction, we see the number 1, this number 1 is to correct the last digit in number . That is: 1.533 + 0.001 = 1.534
So
How to calculate square root without using a calculator
Find the square root of the integer
Find the square root by multiplying.
The square root of a number is the number that when you multiply the number by itself, you will find the first number you have.
That means, “What number can you multiply by itself to get the number you already have?”
For example:
The square root of 1 is 1 because 1 times 1 equals 1 (1 X 1 = 1).
The square root of 4 is 2 because 2 times 2 equals 4 (2 X 2 = 4).
The square root of 9 is 3 because 3 x 3 = 9.
Use division to find square roots
To find the square root of an integer, you can divide the integer by successive numbers until you find a quotient that is exactly the same as your divisor.
For example:
16 divided by 4 is 4, so 4 is the square root of 16.
4 divided by 2 is 2, so 2 is the square root of 4.
Find the square roots of other numbers
Guess and then use the method of elimination
Example: Find the square root of 20.
Meanwhile, we know that 16 is a perfect square number with a square root of 4 (4X4=16).
25 also has a square root of 5 (5X5=25).
So we would guess that the square root of 20 would be between 4 and 5.
We can guess that the square root of 20 is 4.5 and try squaring 4.5 to check. That is, take 4.5 x 4.5. If the answer does not come out 20, we see if the result is greater or less than 20 to calculate. If it is less than 20, we try again with 4, 6 and larger numbers. If the result is greater than 20, then we try calculating with 4,4 and smaller numbers until we get the correct result.
The result in this calculation is 4.475 X 4.475 = 20.03. When you round down, the answer is 20.
How to compare square roots
For any two positive numbers a and b
If a = b then
If a > b then 
If a
For example:
Compare and
Because 21
Hopefully the above article has helped you grasp the knowledge of square roots, how to calculate, how to compare… so that you can solve square root exercises as well as other related exercises.
