The square root of 169 is a value that, when multiplied by itself, gives the original number, 169. To find the square root of 169, we can use various mathematical methods, including factoring, the use of a calculator, or simply recalling perfect squares. Among these methods, recalling perfect squares is the most straightforward approach for this particular number.
Understanding Perfect Squares
Perfect squares are numbers that can be expressed as the square of an integer. For example, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 161, and 169 are the first few perfect squares. Recognizing these numbers can help in quickly identifying the square roots of perfect squares.
Calculating the Square Root of 169
To calculate the square root of 169, we look for the number that, when squared (multiplied by itself), equals 169. From the list of perfect squares mentioned earlier, we find that 13 squared (13^2) equals 169. Therefore, the square root of 169 is 13.
| Number | Square |
|---|---|
| 12 | 144 |
| 13 | 169 |
| 14 | 196 |
Key Points
- The square root of 169 is 13, because 13^2 = 169.
- Recognizing perfect squares can simplify the process of finding square roots.
- The square root of a number can be both positive and negative, as both will result in a positive number when squared.
- In mathematical terms, if y = x^2, then the square root of y is x, and it can also be -x, since (-x)^2 = x^2 = y.
- Calculators and computational tools can also be used to find square roots, especially for numbers that are not perfect squares.
In conclusion, finding the square root of 169 involves understanding perfect squares and recognizing that 13 is the number that, when squared, equals 169. This method is straightforward for perfect squares, but for other numbers, additional mathematical techniques or tools may be necessary.
What is the definition of a perfect square?
+A perfect square is a number that can be expressed as the square of an integer. For example, 1, 4, 9, 16 are perfect squares because they are the squares of the integers 1, 2, 3, and 4, respectively.
How do you find the square root of a number that is not a perfect square?
+For numbers that are not perfect squares, finding the square root often requires the use of a calculator or computational tool. These tools can provide an approximate value of the square root. In some cases, mathematical methods like long division or algebraic techniques can also be used.
Can the square root of a number be negative?
+Yes, the square root of a number can be negative. In fact, every positive number has two square roots, one positive and one negative, because both the positive and negative square roots, when squared, give the original positive number.
