Square Root of 47
2026-02-28 17:51 Diff
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Last updated on August 5, 2025

If a number is multiplied by the same number, the result is a square. The inverse of the square is a square root. The square root is used in fields such as vehicle design, finance, etc. Here, we will discuss the square root of 47.

What is the Square Root of 47?

The square root is the inverse of the square of the number. 47 is not a perfect square. The square root of 47 is expressed in both radical and exponential form.

In the radical form, it is expressed as √47, whereas (47)^(1/2) in the exponential form. √47 ≈ 6.85565, which is an irrational number because it cannot be expressed in the form of p/q, where p and q are integers and q ≠ 0.

Finding the Square Root of 47

The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers, the long division method and approximation method are used. Let us now learn the following methods: Prime factorization method Long division method Approximation method

Square Root of 47 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 47 is broken down into its prime factors:

Step 1: Finding the prime factors of 47 47 is a prime number, so it can only be divided by 1 and 47. Since 47 is not a perfect square, calculating √47 using prime factorization does not provide an exact integer result.

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Square Root of 47 by Long Division Method

The long division method is particularly used for non-perfect square numbers. In this method, we check the closest perfect square numbers for the given number. Let us now learn how to find the square root using the long division method, step by step.

Step 1: To begin with, group the numbers from right to left. For 47, we consider it as a whole number since it is less than 100.

Step 2: Find the largest number whose square is less than or equal to 47. We can say n as '6' because 6×6 = 36, which is less than 47. Now the quotient is 6, and after subtracting 36 from 47, the remainder is 11.

Step 3: Bring down a pair of zeroes, making the new dividend 1100. Add the old divisor with the same number (6+6) to get 12, which will be our new divisor.

Step 4: Find 'n' such that 12n × n ≤ 1100. In this case, n is 8, as 128×8 = 1024.

Step 5: Subtract 1024 from 1100, resulting in a remainder of 76. The quotient is now 6.8.

Step 6: Continue this process by bringing down more pairs of zeroes and finding the next digit. Following these steps, you continue until you achieve the desired level of accuracy.

The square root of 47 is approximately 6.855.

Square Root of 47 by Approximation Method

The approximation method is another method for finding the square roots; it is an easy method to find the square root of a given number. Now let us learn how to find the square root of 47 using the approximation method.

Step 1: Find the closest perfect squares of √47. The closest perfect squares are 36 (6²) and 49 (7²). √47 falls somewhere between 6 and 7.

Step 2: Apply the formula: (Given number - smaller perfect square) / (Larger perfect square - smaller perfect square)

Using the formula (47 - 36) ÷ (49 - 36) = 11/13 ≈ 0.846 Adding this to the smaller root: 6 + 0.846 = 6.846, so the square root of 47 is approximately 6.855.

Common Mistakes and How to Avoid Them in the Square Root of 47

Students may make mistakes while finding the square root, such as forgetting about the negative square root or skipping long division steps. Now let us look at a few common mistakes in detail.

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Problem 1

Can you help Max find the area of a square box if its side length is given as √47?

Okay, lets begin

The area of the square is 47 square units.

Explanation

The area of a square is calculated as side².

The side length is given as √47.

Area of the square = side² = √47 × √47 = 47

Therefore, the area of the square box is 47 square units.

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Problem 2

A square-shaped building measuring 47 square feet is built; if each of the sides is √47, what will be the square feet of half of the building?

Okay, lets begin

23.5 square feet

Explanation

We can just divide the given area by 2 since the building is square-shaped.

Dividing 47 by 2 gives us 23.5.

So half of the building measures 23.5 square feet.

Well explained 👍

Problem 3

Calculate √47 × 3.

Okay, lets begin

20.56695

Explanation

The first step is to find the square root of 47, which is approximately 6.855, and then multiply it by 3.

So, 6.855 × 3 ≈ 20.56695.

Well explained 👍

Problem 4

What will be the square root of (47 + 2)?

Okay, lets begin

The square root is approximately 7.

Explanation

To find the square root, we need to find the sum of (47 + 2), which equals 49.

The square root of 49 is 7.

Therefore, the square root of (47 + 2) is ±7.

Well explained 👍

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √47 units and the width ‘w’ is 5 units.

Okay, lets begin

The perimeter of the rectangle is approximately 23.7113 units.

Explanation

Perimeter of the rectangle = 2 × (length + width)

Perimeter = 2 × (√47 + 5) = 2 × (6.855 + 5) ≈ 2 × 11.855 = 23.7113 units.

Well explained 👍

FAQ on Square Root of 47

1.What is √47 in its simplest form?

The prime factorization of 47 is just 47 itself as it is a prime number, so the simplest form of √47 is itself, √47.

2.Mention the factors of 47.

Factors of 47 are 1 and 47 since it is a prime number.

3.Calculate the square of 47.

We get the square of 47 by multiplying the number by itself, that is 47 × 47 = 2209.

4.Is 47 a prime number?

Yes, 47 is a prime number as it has only two factors: 1 and 47.

5.47 is divisible by?

47 is only divisible by 1 and 47.

Important Glossaries for the Square Root of 47

  • Square root: A square root of a number is one of the two equal factors of the number. For example, 4² = 16, and the inverse operation is the square root, which is √16 = 4.
     
  • Irrational number: An irrational number cannot be written as a simple fraction (p/q) where q ≠ 0. For example, √47 is irrational.
     
  • Prime number: A prime number is a number greater than 1 with no divisors other than 1 and itself. For example, 47 is a prime number.
     
  • Decimal approximation: A method of expressing numbers by using a finite sequence of digits after the decimal point to approximate values like √47 ≈ 6.855.
     
  • Perfect square: A perfect square is an integer that is the square of an integer. For example, 49 is a perfect square because it is 7².

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Jaskaran Singh Saluja

About the Author

Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.

Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.