square root of 144

What does square root of 144 mean?

The square root of 144 represents the value that, when multiplied by itself, gives the result of 144. In other words, it is the number that, when squared, equals 144.

What is the answer to square root of 144?

The answer to the square root of 144 is 12.

Is square root of 144 a rational number or an irrational number?

The square root of 144 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 144 is a perfect square, its square root is a rational number.

To further explain, the square root of 144 can be simplified as √144 = √(12^2) = 12. Since 12 can be expressed as the fraction 12/1, it is a rational number.

Solving methods for square root of 144

There are several methods to solve for the square root of 144. Here, we will discuss two common methods: prime factorization and using a calculator.

Prime Factorization Method

1. Begin by finding the prime factors of 144: 2 * 2 * 2 * 2 * 3 * 3.
2. Group the prime factors in pairs: (2 * 2) * (2 * 2) * (3 * 3).
3. Take one factor from each pair and multiply them together: 2 * 2 * 3 = 12.
4. The result, 12, is the square root of 144.

Calculator Method

1. Enter 144 into a calculator.
2. Press the square root (√) button.
3. The result displayed will be 12, which is the square root of 144.

Solved examples of square root of 144

1. √144 = 12
2. √(144 + 36) = √180 = 6√5
3. √(144 - 100) = √44 = 2√11

In the first example, the square root of 144 is simply 12. In the second example, we can simplify the square root of 180 by breaking it down into the square root of 36 times the square root of 5. Since the square root of 36 is 6, the final result is 6√5. In the third example, we subtract 100 from 144 and take the square root of the result, which simplifies to 2√11.

What does square root mean in mathematics?

In mathematics, the square root of a number is a value that, when multiplied by itself, gives the original number. It is denoted by the symbol √. The square root is the opposite operation of squaring a number.

For example, the square root of 9 is 3 because 3 * 3 = 9. Similarly, the square root of 16 is 4 because 4 * 4 = 16.

Square root formula

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

√x = y

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

Symbols used to represent square root

The symbol √ is used to represent the square root in mathematics. It is placed in front of the number or expression for which we want to find the square root.

For example, √25 represents the square root of 25.

Types of square roots

There are two types of square roots: positive and negative.

The positive square root (√x) represents the principal square root, which is the positive value that, when squared, gives the original number.

The negative square root (-√x) represents the negative value that, when squared, gives the original number.

For example, the positive square root of 25 is 5 (√25 = 5), and the negative square root of 25 is -5 (-√25 = -5).

FAQs on square root of 144

Question: What is the square root of 144?

Answer: The square root of 144 is 12.

Question: Is the square root of 144 a rational number?

Answer: Yes, the square root of 144 is a rational number.

Question: Can the square root of 144 be simplified?

Answer: No, the square root of 144 is already in its simplest form as 12.

Question: What is the square root of a negative number, such as -144?

Answer: The square root of a negative number is not a real number. It is represented by the imaginary unit "i" and is beyond the scope of this discussion.