square root of 400

What does square root of 400 mean?

The square root of 400 is a mathematical operation that determines the value which, when multiplied by itself, equals 400. In other words, it finds the number that, when squared, gives a result of 400.

What is the answer to square root of 400?

The answer to the square root of 400 is 20.

Is square root of 400 a rational number or an irrational number?

The square root of 400 is a rational number. A rational number is any number that can be expressed as a fraction, where the numerator and denominator are both integers. Since 20 can be written as 20/1, it is a rational number.

Solving methods for square root of 400

There are several methods to solve for the square root of 400. 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 400, which are 2 * 2 * 2 * 2 * 5 * 5.
2. Group the prime factors into pairs: (2 * 2) * (2 * 2) * (5 * 5).
3. Take one number from each pair and multiply them together: 2 * 2 * 5 = 20.
4. The result, 20, is the square root of 400.

Long Division Method:

1. Start by assuming a number as the square root of 400, for example, 20.
2. Divide 400 by 20: 400 ÷ 20 = 20.
3. Take the average of the result and the assumed number: (20 + 20) ÷ 2 = 20.
4. Repeat steps 2 and 3 until the result remains the same.
5. The final result, 20, is the square root of 400.

More than 3 solved examples about square root of 400 and detailed explanation

Example 1: To find the square root of 400, we can use the prime factorization method.

1. Prime factors of 400 are 2 * 2 * 2 * 2 * 5 * 5.
2. Grouping them into pairs: (2 * 2) * (2 * 2) * (5 * 5).
3. Taking one number from each pair and multiplying them together: 2 * 2 * 5 = 20.
4. Therefore, the square root of 400 is 20.

Example 2: Using the long division method to find the square root of 400.

1. Assume the square root of 400 as 20.
2. Divide 400 by 20: 400 ÷ 20 = 20.
3. Take the average of 20 and 20: (20 + 20) ÷ 2 = 20.
4. The result remains the same, so the square root of 400 is 20.

Example 3: Using the long division method again.

1. Assume the square root of 400 as 25.
2. Divide 400 by 25: 400 ÷ 25 = 16.
3. Take the average of 25 and 16: (25 + 16) ÷ 2 = 20.5.
4. Repeat step 2 and 3 until the result remains the same.
5. The final result is 20.5, which is an approximation of the square root of 400.

What do 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 25 is 5 because 5 * 5 = 25.

Square root formula

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

√x = x^(1/2)

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, while the negative square root represents the opposite value. For example, the positive square root of 25 is 5, and the negative square root of 25 is -5.

FAQs on square root of 400

Q: What is the square root of 400? A: The square root of 400 is 20.

Q: Is the square root of 400 a rational number? A: Yes, the square root of 400 is a rational number.

Q: How can I calculate the square root of 400? A: You can calculate the square root of 400 using methods like prime factorization or long division.

Q: What does the square root of 400 represent? A: The square root of 400 represents the value that, when multiplied by itself, equals 400.