Find the square root of 169.

To find the square root of 169, we need to identify a number that, when multiplied by itself, equals 169. In this case, the square root of 169 is 13, because 13 times 13 equals 169. This can be expressed mathematically as:

Understanding Square Roots

A square root of a number is a value that, when squared (multiplied by itself), gives the original number. The symbol for square root is √. So, we can write:

√169 = 13

Breaking It Down

To further clarify how we arrive at this answer, let's consider the process:

• First, we can list the perfect squares that are close to 169. These include:
• 1² = 1
• 2² = 4
• 3² = 9
• 4² = 16
• 5² = 25
• 6² = 36
• 7² = 49
• 8² = 64
• 9² = 81
• 10² = 100
• 11² = 121
• 12² = 144
• 13² = 169
• From this list, we can see that 13 is the number we are looking for.

Visualizing the Concept

Imagine a square with an area of 169 square units. The length of each side of this square would be the square root of the area. Since the area is 169, each side measures 13 units. This visual representation helps solidify the concept of square roots.

Practical Applications

Understanding square roots is essential in various fields, including mathematics, engineering, and physics. For instance, in geometry, calculating the dimensions of shapes often involves square roots. In real life, if you're trying to determine the side length of a square garden that has an area of 169 square feet, knowing that the side length is 13 feet allows you to plan accordingly.

In summary, the square root of 169 is 13, and this concept is foundational in mathematics, helping us understand relationships between numbers and their geometric representations.