**What Is The Square Root Of 37** – A square root is a term used to find the 1/2 power of a number, which can also be written as √ (where √ is the subscript or square root symbol). In this article, we’re going to calculate the square root of 148, which is √148. If there are decimals, we can say that it is not a perfect square number.

In this article, we will analyze and find the square root of 148 using various mathematical methods, such as the approximation method and the long division method.

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## What Is The Square Root Of 37

A square root can be defined as a quantity that can be doubled to produce the square of the same quantity. In simple terms, it can be explained as follows:

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The square can be removed by the square root because it equals 1/2; so get 12,165. So 12,165 is the square root of 148. The square root produces both positive and negative integers.

You can calculate the square root of 148 using one of two methods that are common in mathematics; one is the approximation method and the other is the long division method.

The √ symbol is interpreted as 1/2 of 148. So multiplying any number by itself yields the square, and taking the square root of any squared yields a real number.

The process of long division is one of the most common methods used to find the square root of a given number. It is easy to understand and gives more reliable and accurate answers. The long division method reduces a multi-digit number to its equal parts.

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Learning how to find the square root of a number using long division is easy. You only need five basic operations: divide, multiply, subtract, subtract, or increment, then repeat.

Follow these simple steps to find the square root of 148 using long division:

Divide 148 from the right side of the number into pairs like 48 and 1.

Now divide the digit 1 by the number and give 1 or any number less than 1. Therefore, in this case, the remainder is zero and the denominator is 1.

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Then reduce the next pair to 48. Now the dividend is equal to 48. To find the next divisor, double the quotient obtained earlier. 1 multiplied by 2; so let’s think of it as the next denominator.

Now multiply by the denominator and pair 2 with another number to make a new denominator, which is $leq$48.

Adding 2 to the denominator and multiplying 22 by 2 gives 44 $leq$ 48. The resulting remainder is 4. Move the next zero pair down and repeat the above process.

Solve to two decimal places until a remainder of zero is obtained or the division process continues indefinitely.

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The resulting quotient of 12,165 is the square root of 148. Figure 1 below describes the long division process:

The approximation method involves taking the square root of an incomplete square number by dividing it by a perfect square less or greater than that number and taking the average.

Follow the detailed steps to find the square root of 148 using the approximation method.

Now take the average of 12 and 12.33. The resulting number is approximately equal to the square root of X.

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148 is not a perfect square. A number is a perfect square if it is divided into two equal parts or equal integers. If a number is a perfect square, it is also rational.

A number expressed as p/q is called a rational number. All natural numbers are rational numbers. The square root of a complete square is an integer; therefore a perfect square is a rational number.

A number that is not a perfect square is irrational because it is a decimal number. As for 148, it’s not a perfect square. It can be proven as follows:

This shows that 148 is not a perfect square because of the decimals; hence an irrational number a prime number? So it only has 2 factors, 1 and the number itself (37). In this short lesson, let’s learn how to calculate the square root of 37 using long division and approximation methods and how to express the square root of 37 as a simple root.

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The square root of 37 is an irrational number where the decimal places add up to infinity. √37 = 6. 08276253029822 cannot be expressed as a rational number in the form p/q. So the square root of 37 is an irrational number.

There are many ways to calculate the square root of 37 or any other number. Let’s name a few: simple factorization method, approximation method, and long division method.

√37 is between √36 and √49 Obviously, √36 is closer to 6 because we know that 6 × 6 = 36. Use the average method to find the approximate value of √37.

The long division method helps to find a more accurate value of the square root of any number. Let’s see how to find the square root of 37 using long division. Here are the desired steps.

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You can forget concepts by recalling them. with this you will learn visually and be amazed by the results.

The square root of 37 is an irrational number because √37 is a non-terminating decimal number like √37 = 6. 08276253029822.

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