What is square root of 144?

Table of Contents

• What is square root?

• What is a perfect square?

• How do we calculate square root?

• What is Prime Factorization Method?

• What is Long Division Method?

• How to Estimate the Square Root?

• Fun Facts - Square Root of 144

• FAQ - Square Root of 144

What is square root? - Square Root of 144

The term "square root" refers to a mathematical operation that determines the value that, when multiplied by itself, gives the original number. In other words, the square root of a number is a value that, when squared (multiplied by itself), equals the original number. The square root symbol is represented by a radical (√).

What is a perfect square? - Square Root of 144

A perfect square is a number that can be expressed as the square of an integer. In other words, it is a number that has an exact integer square root. When you take the square root of a perfect square, you get a whole number as the result.

For example, 9 is a perfect square because it can be expressed as 3 × 3, where 3 is an integer. Similarly, 16 is a perfect square because it can be expressed as 4 × 4.

Some common examples of perfect squares are 1, 4, 9, 16, 25, 36, 49, and so on.

How do we calculate square root? - Square Root of 144

The square root of a number can be calculated using various methods. Here are two commonly used methods:

1. Prime Factorization Method: This method involves finding the prime factors of the number and grouping them into pairs. Each pair consists of the same prime factor. The product of these pairs gives the square root of the original number.

For example, to calculate the square root of 36 using prime factorization:

The prime factors of 36 are 2, 2, 3, 3.

Grouping them into pairs: (2, 2), (3, 3).

Taking the product of each pair: 2 × 2 × 3 × 3 = 6 × 6 = 36.

So, the square root of 36 is 6.

2. Long Division Method: This method is similar to long division, but it involves finding the square root digit by digit.

For example, to calculate the square root of 36 using prime factorization:

Start by separating the digits into pairs from the right: 8 and 1.

Find the largest digit 'x' such that 'x' multiplied by itself is less than or equal to 8 (the leftmost pair). In this case, 'x' is 2 because 2 × 2 = 4.

Write 2 as the first digit of the square root.

Subtract the square of 2 from 8: 8 - 4 = 4.

Bring down the next pair (1) to the right of 4.

Double the current digit (2) and guess a digit for the next place value. Try 4 (2 multiplied by 2) as a guess.

Multiply the new number (24) by the guessed digit (4): 24 × 4 = 96.

Find the largest single-digit number 'x' that satisfies the condition '2x multiplied by x' is less than or equal to 96. In this case, 'x' is 6 because 26 × 6 = 156.

Write 6 as the next digit of the square root.

Subtract the product (156) from the result (196): 196 - 156 = 40.

Since there are no more pairs, the square root of 81 is 26.

What is Prime Factorization Method? - Square Root of 144

The Prime Factorization Method is a technique used to determine the prime factors of a number. It involves breaking down the given number into its constituent prime factors, which are prime numbers that can divide the original number evenly.

Here's an overview of the Prime Factorization Method:

1. Start with the number you want to find the prime factors of.
2. Begin by dividing the number by the smallest prime number, which is 2. If the number is divisible by 2, divide it repeatedly until it is no longer divisible. Note down each time you divide by 2.
3. Move on to the next prime number, which is 3. If the number is divisible by 3, divide it repeatedly until it is no longer divisible. Note down each time you divide by 3.

Continue this process with successive prime numbers (5, 7, 11, and so on) until the number becomes 1.

The list of all the prime numbers that you noted down during the process is the prime factorization of the original number.

The prime factorization method helps identify all the prime factors of a given number, which can be useful for various purposes such as simplifying fractions, finding the greatest common divisor, or calculating square roots.

What is Long Division Method? - Square Root of 144

The Long Division Method is a mathematical technique used to perform division when the dividend (the number being divided) and divisor (the number dividing the dividend) are relatively large or when an exact quotient is required. This method involves a step-by-step process of dividing the dividend by the divisor, digit by digit, to find the quotient.

Here's a step-by-step explanation of the Long Division Method:

1. Write the dividend (the number being divided) on the left, and the divisor (the number dividing the dividend) on the outside of the division symbol (÷).
2. Start with the leftmost digit of the dividend and divide it by the divisor. Write the quotient (the result of the division) on top of the division symbol, directly above the dividend digit.
3. Multiply the quotient by the divisor and write the result below the dividend, aligned with the corresponding digits.
4. Subtract the product obtained in step 3 from the digits directly above it. Write the difference below the line.
5. Bring down the next digit of the dividend and write it next to the difference obtained in the previous step.
6. Repeat steps 2 to 5 until all the digits in the dividend have been processed.
7. Once the last digit of the dividend has been brought down and processed, the division is complete.

The final result is the quotient obtained from the division.

How to Estimate the Square Root? - Square Root of 144

Estimating the square root of a number involves finding an approximate value that is close to the actual square root. Here's a method to estimate the square root:

1. Identify the nearest perfect square below the given number. This will serve as a reference point for estimation.
2. Determine the difference between the given number and the nearest perfect square found in step 1.
3. Divide the difference obtained in step 2 by twice the reference point (the square root of the perfect square found in step 1).
4. Add the result obtained in step 3 to the reference point to get an estimated value of the square root.

Fun Facts - Square Root of 144

The symbol for the square root (√) was first introduced by the ancient Greek mathematician Heron of Alexandria. He used a special symbol to represent square roots in his work on geometry and engineering, which dates back to around the 1st century AD.

However, the concept of square roots predates Heron of Alexandria by several centuries. The Babylonians, who lived around 2000 BC, had a basic understanding of square roots and used approximation methods to calculate them. The concept of square roots also appeared in the works of ancient Indian mathematicians, such as Aryabhata in the 5th century AD.

The discovery and understanding of square roots have played a significant role in the development of mathematics and have applications in various fields, including engineering, physics, computer science, and cryptography.

FAQ - Square Root of 144

What is the meaning of √?

Square root

What is this √ 2?

The expression √2 represents the square root of 2. It is an irrational number, meaning it cannot be expressed as a fraction (ratio) of two integers and its decimal representation goes on infinitely without repeating.
The square root of 2 is approximately equal to 1.41421356

Why is √ 4 = 2 only?

The square root of 4, denoted as √4, is equal to 2. This is because when you square 2 (multiply it by itself), the result is 4.

How to solve √ 3?

The square root of 3, denoted as √3, is approximately equal to 1.732 when rounded to three decimal places. The long division method can be used to calculate the square root of 3, but it is a non-repeating, irrational number. Its exact value extends infinitely without a pattern. However, for practical purposes, the value of √3 is often approximated as 1.732 to simplify calculations.

What is the square of √ 1?

1

Why √2 is irrational?

The irrationality of the square root of 2 was discovered by the ancient Greeks. They observed that the diagonal of a square with sides measuring 1 unit cannot be expressed as a rational number. Using the Pythagorean Theorem, they determined that the length of the diagonal is equal to the square root of 2. Therefore, it was concluded that the square root of 2 is an irrational number, meaning it cannot be expressed as a fraction or ratio of two integers. The decimal representation of the square root of 2 goes on infinitely without repeating or terminating.

Can I take the square root of 0?

Yes, the answer is 0

Is Infinity a square root?

In mathematics, infinity is not treated as a number, and the concept of taking the square root of infinity does not have a well-defined meaning.

Is root a real number?

The square root of a non-negative real number is a real number, while the square root of a negative real number is a complex number involving the imaginary unit "i."

Is 4 a square root?

No, 4 is not a square root. 4 is a perfect square, meaning that it is the result of squaring a whole number. In this case, 4 is the square of 2, because 2 multiplied by 2 equals 4.