square root of 48

What does square root of 48 mean?

The square root of 48 represents the value that, when multiplied by itself, gives the result of 48. In other words, it is the number that, when squared, equals 48.

What is the answer to square root of 48?

The answer to the square root of 48 is approximately 6.928203230275509... (rounded to 15 decimal places).

Is square root of 48 a rational number or an irrational number?

The square root of 48 is an irrational number. An irrational number is a number that cannot be expressed as a fraction of two integers. The decimal representation of the square root of 48 goes on forever without repeating, indicating that it is irrational.

Solving methods for square root of 48

There are several methods to solve for the square root of 48. Here, we will discuss two common methods: prime factorization and the long division method.

Prime Factorization Method

1. Start by finding the prime factors of 48: 2 * 2 * 2 * 2 * 3.
2. Group the prime factors in pairs: (2 * 2) * (2 * 2) * 3.
3. Take one factor from each pair and multiply them together: 2 * 2 * 3 = 12.
4. The result, 12, is the largest perfect square that divides 48.
5. Therefore, the square root of 48 is the square root of 12 times the square root of 4: √48 = √12 * √4.
6. Simplify the square roots: √48 = 2√3.

Long Division Method

1. Start by assuming a number as the square root of 48, let's say 7.
2. Divide 48 by 7: 48 ÷ 7 = 6.857142857142857...
3. Take the average of 7 and the result from step 2: (7 + 6.857142857142857...) ÷ 2 = 6.928571428571429...
4. Repeat steps 2 and 3 until you reach the desired level of accuracy.
5. The final result is approximately 6.928203230275509...

Solved examples about square root of 48

Example 1: Find the square root of 48.

Using the prime factorization method: √48 = √(2 * 2 * 2 * 2 * 3) = 2 * √3 = 2√3.

Example 2: Simplify √(48/3).

√(48/3) = √(16) = 4.

Example 3: Evaluate (√48)^2.

(√48)^2 = 48.

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 √ and is used to find the side length of a square with a given area or to solve quadratic equations.

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 used to represent the square root in mathematics.

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.

FAQs on square root of 48

Question: What is the square root of 48 in simplified radical form?

The square root of 48 in simplified radical form is 4√3.

Question: Is the square root of 48 a whole number?

No, the square root of 48 is not a whole number. It is an irrational number.

Question: Can the square root of 48 be negative?

Yes, the square root of 48 can be both positive and negative. The positive square root is denoted as √48, while the negative square root is denoted as -√48.