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Last updated on March 20th, 2025

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Square Root of 87

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Foundation
Intermediate
Advance Topics

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 the field of vehicle design, finance, etc. Here, we will discuss the square root of 87.

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What is the Square Root of 87?

The square root is the inverse of the square of the number. 87 is not a perfect square. The square root of 87 is expressed in both radical and exponential form.

In the radical form, it is expressed as √87, whereas (87)(1/2) in the exponential form. √87 ≈ 9.327, 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.

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Finding the Square Root of 87

The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where the long division method and approximation method are used. Let us now learn the following methods:

 

  1. Prime factorization method
  2. Long division method
  3. Approximation method
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Square Root of 87 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 87 is broken down into its prime factors.

 

Step 1: Finding the prime factors of 87 Breaking it down, we get 3 x 29.

 

Step 2: Now we found out the prime factors of 87. The second step is to make pairs of those prime factors. Since 87 is not a perfect square, the digits of the number can’t be grouped in pairs.

 

Therefore, calculating 87 using prime factorization is not possible for finding an exact integer result.

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Square Root of 87 by Long Division Method

The long division method is particularly used for non-perfect square numbers. Let us now learn how to find the square root using the long division method, step by step.

 

Step 1: To begin with, we need to group the numbers from right to left. In the case of 87, we do not need to group since it is a two-digit number.

 

Step 2: Now we need to find n whose square is less than or equal to 87. We can say n as ‘9’ because 9 x 9 = 81, which is less than 87. Now the quotient is 9, and the remainder is 87 - 81 = 6.

 

Step 3: Since the dividend is less than the divisor, add a decimal point to the quotient and bring down a pair of zeroes to the remainder. Now the new dividend is 600.

 

Step 4: Double the quotient (9) and write it as 18. Now find a digit x such that 18x x x is less than or equal to 600. Let's try x = 3, giving us 183 x 3 = 549.

 

Step 5: Subtract 549 from 600, and the remainder is 51. The quotient is now 9.3.

 

Step 6: Continue the process by bringing down more pairs of zeroes until you achieve the desired decimal precision.

 

So the square root of √87 is approximately 9.327.

Professor Greenline from BrightChamps

Square Root of 87 by Approximation Method

The approximation method is an easy method to find the square root of a given number. Now let us learn how to find the square root of 87 using the approximation method.

 

Step 1: Identify the closest perfect squares around 87. The nearest perfect squares are 81 (9^2) and 100 (10^2). √87 falls between 9 and 10.

 

Step 2: Apply the formula: (Given number - smaller perfect square) / (larger perfect square - smaller perfect square) (87 - 81) / (100 - 81) = 6 / 19 ≈ 0.316

 

Adding this to the smaller perfect square root gives us 9 + 0.316 = 9.316,

 

so the square root of 87 is approximately 9.316.

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Common Mistakes and How to Avoid Them in the Square Root of 87

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Square Root of 87 Examples

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Problem 1

Can you help Max find the area of a square box if its side length is given as √87?

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Explanation

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Problem 2

A square-shaped building measuring 87 square feet is built; if each of the sides is √87, what will be the square feet of half of the building?

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Explanation

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Problem 3

Calculate √87 x 5.

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Explanation

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Max, the Girl Character from BrightChamps

Problem 4

What will be the square root of (81 + 6)?

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Explanation

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Max, the Girl Character from BrightChamps

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √87 units and the width ‘w’ is 38 units.

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Explanation

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FAQ on Square Root of 87

1.What is √87 in its simplest form?

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2.Mention the factors of 87.

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3.Calculate the square of 87.

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4.Is 87 a prime number?

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5.87 is divisible by?

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Professor Greenline from BrightChamps

Important Glossaries for the Square Root of 87

  • Square root: A square root is the inverse of a square. Example: 42 = 16, and the inverse of the square is the square root, that is √16 = 4.

 

  • Irrational number: An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero and p and q are integers.

 

  • Principal square root: A number has both positive and negative square roots; however, it is always the positive square root that has more prominence due to its uses in the real world. That is the reason it is also known as the principal square root.

 

  • Long division method: A method used to find the square root of non-perfect squares by dividing the number into groups of two digits from right to left.

 

  • Prime factorization: The process of breaking down a number into its basic prime number factors, which is useful for simplifying radicals.
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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.

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Fun Fact

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

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