The square root of 196 is 14, because 14 × 14 = 196. To find the square root of 196, you look for a number that, when multiplied by itself, equals 196. Since 196 is a perfect square, its square root is a whole number rather than a decimal or irrational value.
Introduction to the Square Root of 196
A square root answers the question: What number multiplied by itself gives the original number? As an example, the square root of 25 is 5 because 5 × 5 = 25. Similarly, the square root of 196 is 14 because 14 × 14 = 196.
In mathematical notation, the square root of 196 is written as:
√196 = 14
Still, it is also important to understand that both 14 and -14 are square roots of 196 because:
14 × 14 = 196
-14 × -14 = 196
The symbol √ usually refers to the principal square root, which means the nonnegative square root. So, √196 = 14, while the solutions to x² = 196 are x = 14 or x = -14 Most people skip this — try not to..
What Does “Square Root” Mean?
A square root is the opposite operation of squaring a number. Squaring means multiplying a number by itself. For example:
- 3² = 3 × 3 = 9
- 6² = 6 × 6 = 36
- 10² = 10 × 10 = 100
So, if you know that a number squared equals 196, you are looking for the original number. Since:
14² = 14 × 14 = 196
then:
√196 = 14
This makes 196 a perfect square. A perfect square is a number that can be expressed as the product of an integer multiplied by itself Still holds up..
Method 1: Using a Square Number List
One simple way to find the square root of 196 is to recall or list common perfect squares.
Here are some perfect squares:
- 10² = 100
- 11² = 121
- 12² = 144
- 13² = 169
- 14² = 196
- 15² = 225
When you look at this list, you can see that 196 appears directly after 169 and before 225. Since 14² = 196, the square root of 196 is 14.
This method is especially useful because 196 is a perfect square. If the number were not a perfect square, such as 195 or 197, the square root would be a decimal. But 196 has a clean whole-number square root And it works..
Method 2: Prime Factorization
Another reliable method is prime factorization. Prime factorization means breaking a number down into its prime factors That's the whole idea..
Start with 196:
196 ÷ 2 = 98
98 ÷ 2 = 49
49 ÷ 7 = 7
7 ÷ 7 = 1
So the prime factorization of 196 is:
196 = 2 × 2 × 7 × 7
This can be written using exponents as:
196 = 2² × 7²
To find the square root, pair the factors:
- 2 × 2 forms one pair
- 7 × 7 forms one pair
For every pair of identical factors, take one factor out of the square root:
√196 = √(2² × 7²)
**√196 = 2
