In math, the square root of a number like 196 is a number that, when multiplied by itself, is equal to 196. We would show this in mathematical form with the square root symbol, which is called the radical symbol: √
Any number with the radical symbol next to it us called the radical term or the square root of 196 in radical form.
To explain the square root a little more, the square root of the number 196 is the quantity (which we call q) that when multiplied by itself is equal to 196:
So what is the square root of 196 and how do we calculate it? Well if you have a computer, or a calculator, you can easily calculate the square root. If you need to do it by hand, then it will require good old fashioned long division with a pencil and piece of paper.
For the purposes of this article, we'll calculate it for you (but later in the article we'll show you how to calculate it yourself with long division). The square root of 196 is 14:
Is 196 a Perfect Square?
When the square root of a given number is a whole number, this is called a perfect square. Perfect squares are important for many mathematical functions and are used in everything from carpentry through to more advanced topics like physics and astronomy.
If we look at the number 196, we know that the square root is 14, and since this is a whole number, we also know that 196 is a perfect square.
If you want to learn more about perfect square numbers we have a list of perfect squares which covers the first 1,000 perfect square numbers.
Is 196 a Rational or Irrational Number?
Another common question you might find when working with the roots of a number like 196 is whether the given number is rational or irrational. Rational numbers can be written as a fraction and irrational numbers can't.
The quickest way to check if a number is rational or irrational is to determine if it is a perfect square. If it is, then it's a rational number, but if it is not a perfect square then it is an irrational number.
We already know that 196 is a rational number then, because we know it is a perfect square.
Calculating the Square Root of 196
To calculate the square root of 196 using a calculator you would type the number 196 into the calculator and then press the √x key:
To calculate the square root of 196 in Excel, Numbers of Google Sheets, you can use the SQRT() function:
Rounding the Square Root of 196
Sometimes when you work with the square root of 196 you might need to round the answer down to a specific number of decimal places:
10th: √196 = 14.0
100th: √196 = 14.00
1000th: √196 = 14.000
Finding the Square Root of 196 with Long Division
If you don't have a calculator or computer software available, you'll have to use good old fashioned long division to work out the square root of 196. This was how mathematicians would calculate it long before calculators and computers were invented.
Step 1
Set up 196 in pairs of two digits from right to left and attach one set of 00 because we want one decimal:
Step 2
Starting with the first set: the largest perfect square less than or equal to 1 is 1, and the square root of 1 is 1 . Therefore, put 1 on top and 1 at the bottom like this:
Step 3
Calculate 1 minus 1 and put the difference below. Then move down the next set of numbers.
Step 4
Double the number in green on top: 1 × 2 = 2. Then, use 2 and the bottom number to make this problem:
2? × ? ≤ 96
The question marks are "blank" and the same "blank". With trial and error, we found the largest number "blank" can be is 4.
Now, enter 4 on top:
Hopefully, this gives you an idea of how to work out the square root using long division so you can calculate future problems by yourself.
Practice Square Roots Using Examples
If you want to continue learning about square roots, take a look at the random calculations in the sidebar to the right of this blog post.
We have listed a selection of completely random numbers that you can click through and follow the information on calculating the square root of that number to help you understand number roots.
Calculate Another Square Root Problem
You could definitely use a calculator or Google.
But if you would like to do this by hand, you can without too much trouble.
Written explanation continues below the video.
It’s possible you recognize that 196 is a perfect square. If you do, but you’re not sure what it is, 196 is definitely an even number. So you can divide by two.
It turns out that 196/2 is 98, which you can also divide by two.
So 2 x 2 x 49 = 196. You should recognize 49 as being a perfect square.
So the square root of 196 simplified is 14.
And it’s good to know that you can square a negative number and the square will be positive.
The convention of saying “the” square root means one, but it’s good to know about multiple solutions.
Additional Problems:
And some numbers that aren’t perfect squares,
Try finding
1. The square root of 20
2. The square root of 228
3. The square root of 52
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You could definitely use a calculator or Google. But if you would like to do this by hand, you can without too much trouble. It’s possible you recognize that 196 is a perfect square. If you do, but you’re not sure what it is, 196 is definitely an even number. So you can divide by two. It turns out that 196/2 is 98, which you can also divide by two. So 2 x 2 x 49 = 196. You should recognize 49 as being a perfect square. And it’s good to know that you can square a negative number and the square will be positive. The convention of saying “the” square root means one, but it’s good to know about multiple solutions.
The arithmetic value which is used for representing the quantity and used in making calculations are defined as Numbers. A symbol like “4, 5, 6” which represents a number is known as numerals. Without numbers, counting things is not possible, date, time, money, etc. these numbers are also used for measurement and used for labeling. The properties of numbers make them helpful in performing arithmetic operations on them. These numbers can be written in numeric forms and also in words.
For example, 3 is written as three in words, 35 is written as thirty-five in words, etc. Students can write the numbers from 1 to 100 in words to learn more. There are different types of numbers, which we can learn. They are whole and natural numbers, odd and even numbers, rational and irrational numbers, etc
Number System
A Number System is a method of showing numbers by writing, which is a mathematical way of representing the numbers of a given set, by using the numbers or symbols in a mathematical manner. The writing system for denoting numbers using digits or symbols in a logical manner is defined as Number System. The digits from 0 to 9 form all the numbers. With these digits, anyone can create infinite numbers. For example, 156,3907, 3456, 1298, 784859, etc
Square root
The value of a number of square roots, which on multiplication by itself gives the original number. Suppose, a is the square root of b, then it is represented as a = √b or we can express the same equation as a2 = b. Here,’√’ this symbol we used to represent the root of numbers is termed as radical. The positive number when it is to be multiplied by itself represents the square of the number. The square root of the square of any positive number gives the original number.
For example, the square of 4 is 16, 42 = 16, and the square root of 16, √16 = 4. Since 4 is a perfect square and we have both the negative and positive square root value of 16 is ±4,means 16 has two square roots one is 4 and second is -4, because 4 x 4 = -4 x -4 = 16. Hence it is easy to find the square root of such numbers, but for an imperfect square, it’s really tricky.
Square Root is represented as ‘√’. It is called a radical symbol. To represent a number ‘a’ as a square root using this symbol can be written as: ‘√a‘, where a is the number. The number here under the radical symbol is called the radicand. For example, the square root of 4 is also represented as a radical of 4. Both represent the same value, and the formula to find the square root is: b = √a
Properties of Square Roots
It is defined as a one-to-one function that takes a positive number as an input and returns the square root of the given input number. For example, here if x = 9, then the function returns the output value as 3.
f(x) = √x
- If a number is a perfect square number, then there definitely exists a perfect square root.
- If a number ends with an even number of zeros (0’s), then we can have a square root.
- The two square root values can be multiplied. For example, √3 can be multiplied by √2, then the result will be √6.
- When two same square roots are multiplied, then the result must be a radical number. It shows that the result is a non-square root number. For example, when √7 is multiplied by √7, the result obtained is 7.
- The square root of negative numbers is undefined. hence the perfect square cannot be negative.
- Some of the numbers end with 2, 3, 7, or 8 (in the unit digit), then the perfect square root does not exist.
- Some of the numbers end with 1, 4, 5, 6, or 9 in the unit digit, then the number will have a square root.
It is easy to find the square root of a number that is a perfect square.
Perfect squares
Perfect squares are those positive numbers or negative numbers that can be written as the multiplication of a number by itself, or you can say that a perfect square is a number which is the value of power 2 of any integer. The number can be expressed as the product of two equal integers. For example, 16 is a perfect square because it is the product of two equal integers, 4 × 4 = 16. or -4 × -4 = 16, However, 24 is not a perfect square because it cannot be expressed as the product of two equal integers. (8 × 3 = 24).
The number which is obtained by squaring a whole number is termed as a Perfect square.
Assume N is a perfect square of a whole number y, this can be written as N = the product of y and y = y2. So, the perfect square formula can be expressed as,
N = Y2
Let’s Use the formula with values.
If y = 5, and N = y2
This means, N = 52 = 25 or (- 5)2= 25
Here, 5 is the positive and negative square root of 25 i.e ±5
therefore there are two square roots of 25: 5 or -5
With the help of square roots, It is easy to identify whether a number is a perfect square or not. If the square root is a whole number then the given number will be a perfect square, and if the square root value is not a whole number, then the given number is not a perfect square.
Solution:
Here square root of 196 is 14, which can be written as ±14,
So, 14 and -14 are the two square roots of 19, n its a perfect square of 196.
And √196 = 14 or 142 = 14 × 14 = 196
Same √196 = 14 or (-14)2= -14 × -14 = 196.
Similar Problems
Question 1: What are the two square roots of 4225?
Solution:
Here 65 is the square root of 4225
±65 are the square root of 4225
So 65 and – 65 are the two square root of 4225.
Question 2: what are the two square roots of 900?
Solution:
Here 900 is the perfect square of 30
302 = 30 × 30 = 900
Or we can write as (-30)2 = (-30) × (-30) = 900
So 30 and -30 are the two square roots of 900.
i.e √900 = ±30
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