Question

Find each square root. Round to the nearest tenth, if necessary. \(\sqrt{196}\)

Short answer

The square root of 196 is 14.

Step-by-step solution

Understanding the Problem

We need to find the square root of 196. The square root of a number is a value that, when multiplied by itself, gives the original number.

Identifying Perfect Squares

Before calculating, we should determine if 196 is a perfect square, meaning it should be the square of an integer.

Calculating the Square Root

By trial or using a calculator, we can determine that the square root of 196 is 14, because \[ 14 \times 14 = 196 \]

Conclusion

Since 196 is a perfect square, the square root is exactly 14. Hence, no need to round as 14 is already an integer.

Key concepts

Perfect Square

A perfect square is a number that can be expressed as the product of an integer with itself. For example, if you multiply the integer 4 by itself, the result is 16, which is a perfect square. This concept helps simplify the process of finding square roots in many mathematics problems. A perfect square always has an integer as its square root, meaning no decimals or fractions are involved.
Identifying perfect squares is useful because it tells you that there is a straightforward answer to the square root. To determine if a number, like 196, is a perfect square, one can try to find an integer that, when multiplied by itself, equals the number. In the case of 196, it is a perfect square because 14 multiplied by 14 equals 196. This means that the square root of 196 is simply 14, making calculations easy.

Integer

An integer is a whole number, and it can be positive, negative, or zero. Integers do not include fractions or decimals. In the realm of square roots and perfect squares, integers play a crucial role. When a number is a perfect square, its square root will also be an integer.
In our exercise with the number 196, we found that the square root is 14. This number is an integer, making it a simple whole number solution without any need for rounding. Understanding integers helps you predict outcomes in math problems, especially when verifying whether numbers are perfect squares and exploring their square roots.

Mathematics Problem Solving

Mathematics problem solving involves breaking down complex problems into manageable steps. Each step should move you closer to a solution. In finding the square root of a number, begin by checking if the number is a perfect square. This can significantly reduce the difficulty of the problem.
Here's a simple way to approach problems like finding the square root of 196:

• Identify if the number is a perfect square by checking if it's the product of an integer by itself.
• If it is a perfect square, the solution is the integer itself, without any extra steps.
• If it’s not a perfect square, use approximation techniques or a calculator to find the square root and round as necessary.

By following these problem-solving steps, mathematics becomes less overwhelming, enabling students to solve exercises systematically and efficiently.