Learn what the square root of 63 is, how to calculate it, its properties, and real-life applications in this informative article.

## Introduction

In mathematics, square roots are an essential concept that is used to solve various problems. The square root of 63 is a perfect example of how this concept is applied, and understanding it is crucial for anyone looking to excel in math. In this article, we will take a deep dive into what the square root of 63 is, how to calculate it, its properties, and real-life applications.

## Definition of Square Root

The square root of a number is a value that, when multiplied by itself, gives the original number. It is denoted by the symbol √. For example, the square root of 16 is 4, as 4 × 4 = 16. The square root of 63 is a bit more complicated to calculate, but we will explore that later in the article.

Calculating square roots is crucial in various fields, including engineering, physics, and finance. It is used to solve problems that involve finding the length of a side of a square or rectangle, calculating the distance between two points, and calculating the area of a circle, among others.

To calculate the square root of a number, we need to find the value that, when multiplied by itself, gives us the original number. This can be done using various methods, including the prime factorization method, long division method, or using a calculator. We will explore the most straightforward method of calculating the square root of 63 in the next section.

## Calculation of Square Root of 63

To calculate the square root of 63, we can use the long division method. Here’s how:

- Write the number 63 as a two-digit number by placing a bar above the tens and units digits: 6|3.
- Find the largest number whose square is less than or equal to 6, which is 2. Write this number on top of the bar as the first digit of the square root: √63 = 2_.
- Subtract the square of the first digit from the number under the bar and bring down the next pair of digits. The result is 63 – 4 = 59. Write 59 next to the remainder.
- Double the first digit and write it as the divisor next to the remainder. In this case, 2 × 2 = 4, so we write 4 next to 59, giving us 594.
- Find the largest number that, when multiplied by the divisor, gives a number less than or equal to 594. This number is 14, and we write it as the next digit of the square root.
- Multiply the new divisor by the last digit and subtract the result from the remainder, which gives us a new remainder. In this case, 14 × 4 = 56, and 594 – 56 = 538. Bring down the next pair of digits, which is 00.
- Double the last digit of the square root and write it as the new divisor. In this case, 84 is the new divisor.
- Repeat steps 5 to 7 until you have the desired level of accuracy.

After repeating the above steps, we get the square root of 63 as 7.937.

## Calculation of Square Root of 63 (Continued)

Calculating the square root of 63 using the long division method may seem complicated at first, but with practice, it can become more manageable. One way to simplify the process is by using diagrams. For example, we can draw a square with an area of 63 and divide it into smaller squares. From here, we can count the number of smaller squares on one side to find the square root of 63.

Another way to find the square root of 63 is by using a calculator. Most scientific calculators have a square root function that can give you the answer quickly. Simply type in 63 and press the square root button to get the answer, which is 7.937.

Knowing how to calculate the square root of 63 is essential, but understanding the properties of square roots can make solving problems involving them much more manageable.

## Properties of Square Roots

The product rule of square roots states that the square root of the product of two numbers is equal to the product of their square roots. In other words, √(a × b) = √a × √b. For example, the square root of 12 can be written as the product of the square roots of 4 and 3: √12 = √4 × √3.

The quotient rule of square roots states that the square root of the quotient of two numbers is equal to the quotient of their square roots. In other words, √(a/b) = √a / √b. For example, the square root of 16 divided by 4 can be written as the quotient of the square roots of 16 and 4: √(16/4) = √16 / √4.

The power rule of square roots states that the square root of a number raised to a power is equal to the number raised to half that power. In other words, √(a^b) = a^(b/2). For example, the square root of 16 raised to the power of 3 can be written as 16^(3/2).

Knowing these rules can help us simplify square roots, making them easier to calculate. For example, if we want to simplify the square root of 27, we can write it as the product of the square root of 3 and the square root of 9: √27 = √3 × √9 = 3√3.

In conclusion, understanding the properties of square roots can make solving problems involving them much more manageable. By applying the product, quotient, and power rules, we can simplify square roots and make them easier to calculate.

## Real-Life Applications of Square Roots

Square roots find extensive use in various fields, including engineering and finance. In engineering, square roots are used to calculate the distance between two points, the area of a circle, the length of a side of a square or rectangle, and much more. For example, when designing a bridge, engineers use square roots to calculate the maximum weight that the bridge can handle, which is critical for the bridge’s safety. They also use square roots to calculate the force required to lift heavy objects using cranes or other lifting devices.

In finance, square roots are used in calculating the standard deviation of a stock portfolio, which measures the risk associated with the portfolio. The standard deviation is a crucial metric for investors as it helps them make informed decisions about their investments. Square roots are also used in mortgage calculations when determining monthly payments and the total amount of interest to be paid over the life of the loan.

## Conclusion

In conclusion, square roots are an essential concept in mathematics that finds extensive use in various fields. Understanding square roots is crucial for those looking to excel in math and fields that use math, such as engineering and finance. In this article, we explored what the square root of 63 is, how to calculate it, its properties, and real-life applications. We hope that this article has been informative and has helped you understand the importance of square roots. For those looking to learn more about this concept, there are many resources available, including textbooks, online courses, and video tutorials. Keep practicing, and you’ll soon become an expert at calculating square roots!