square root of 169

What does square root of 169 mean?

The square root of a number is a value that, when multiplied by itself, gives the original number. In the case of the square root of 169, it means finding a number that, when multiplied by itself, equals 169.

What is the answer to square root of 169?

The answer to the square root of 169 is 13.

Is square root of 169 a rational number or an irrational number?

The square root of 169 is a rational number. A rational number is a number that can be expressed as a fraction, where both the numerator and denominator are integers. Since 13 can be expressed as 13/1, it is a rational number.

Solving methods for square root of 169

There are several methods to solve for the square root of 169. Here, we will discuss two common methods: the prime factorization method and the long division method.

Prime Factorization Method:

1. Begin by finding the prime factors of 169. The prime factors of 169 are 13 and 13.
2. Group the prime factors in pairs: (13, 13).
3. Take one number from each pair and multiply them together: 13 * 13 = 169.
4. The result is the square root of 169, which is 13.

Long Division Method:

1. Start by assuming a number as the square root of 169. Let's assume it to be 10.
2. Divide 169 by 10: 169 ÷ 10 = 16.9.
3. Average the result with the assumed number: (10 + 16.9)/2 = 13.45.
4. Repeat steps 2 and 3 until you reach a desired level of accuracy.
5. The final result is the square root of 169, which is 13.

More than 3 solved examples about square root of 169

Example 1: To find the square root of 169, we can use the prime factorization method. The prime factors of 169 are 13 and 13. Taking one number from each pair and multiplying them together: 13 * 13 = 169. Therefore, the square root of 169 is 13.

Example 2: Using the long division method, let's find the square root of 169. Assuming the square root to be 10, we divide 169 by 10: 169 ÷ 10 = 16.9. Taking the average of 10 and 16.9: (10 + 16.9)/2 = 13.45. We repeat the process until we reach the desired level of accuracy. After a few iterations, we find that the square root of 169 is approximately 13.

Example 3: Another way to find the square root of 169 is by using a calculator. Entering the number 169 and pressing the square root button gives us the result of 13.

What do square root mean in mathematics?

In mathematics, the square root of a number represents the value that, when multiplied by itself, gives the original number. It is denoted by the symbol √. The square root is a fundamental concept in mathematics and is used in various fields, such as geometry, algebra, and calculus.

Square root formula

The square root of a number can be calculated using the formula:

√x = y

Where x is the number for which we want to find the square root, and y is the square root of x.

What symbols are used to represent square root?

The symbol √ is commonly used to represent the square root in mathematics. For example, √25 represents the square root of 25.

What are the types of square roots?

There are two types of square roots: positive square roots and negative square roots. The positive square root represents the principal square root, denoted by √x, and it gives the positive value of the square root. The negative square root, denoted by -√x, gives the negative value of the square root.

FAQs on square root of 169

Question: What is the square root of 169? Answer: The square root of 169 is 13.

Question: Is the square root of 169 a rational number? Answer: Yes, the square root of 169 is a rational number.

Question: Can the square root of 169 be simplified further? Answer: No, the square root of 169 is already in its simplest form.

Question: What is the square of the square root of 169? Answer: The square of the square root of 169 is equal to 169.

Question: Can the square root of 169 be negative? Answer: No, the square root of 169 is always positive.