What is the square root of 196
The Correct Answer and Explanation is:
The square root of 196 is 14.
Explanation:
The square root of a number is a value that, when multiplied by itself, gives the original number. For 196, the equation is:
[
\sqrt{196} = x \quad \text{where } x \times x = 196
]
To find this value, consider the following steps:
- Break Down 196:
Start by identifying the factors of 196. It can be written as:
[
196 = 14 \times 14
]
This immediately shows that ( 14 \times 14 = 196 ), meaning 14 is the square root of 196. - Prime Factorization Method:
Alternatively, break 196 into its prime factors:
[
196 \div 2 = 98 \quad (\text{divide by 2, the smallest prime number})
]
[
98 \div 2 = 49 \quad (\text{divide by 2 again})
]
[
49 \div 7 = 7 \quad (\text{divide by 7, another prime number})
]
[
7 \div 7 = 1
]
The prime factors of 196 are ( 2 \times 2 \times 7 \times 7 ), which can be grouped as:
[
(2 \times 7) \times (2 \times 7) = 14 \times 14
]
Therefore, ( \sqrt{196} = 14 ). - Perfect Square Property:
A perfect square is a number that has an integer as its square root. Since ( 14^2 = 196 ), 196 is a perfect square, and its square root is 14. - Verification:
Multiply ( 14 \times 14 ) to confirm:
[
14 \times 14 = 196
]
Understanding square roots is essential in mathematics, especially in geometry, algebra, and real-world applications such as calculating areas, analyzing physics problems, and financial modeling. By recognizing that 196 is a perfect square, finding its square root becomes straightforward.