Square Root of 87
2026-02-28 06:06 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 the field of vehicle design, finance, etc. Here, we will discuss the square root of 87.

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.

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

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.

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.

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

Students often make mistakes while finding the square root, such as forgetting about the negative square root, skipping the long division method, etc. Now let us look at a few mistakes that students tend to make 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 √87?

Okay, lets begin

The area of the square is approximately 87 square units.

Explanation

The area of the square = side2. The side length is given as √87. Area of the square = side2 = √87 x √87 = 87.

Therefore, the area of the square box is approximately 87 square units.

Well explained 👍

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?

Okay, lets begin

43.5 square feet

Explanation

We can just divide the given area by 2 as the building is square-shaped. Dividing 87 by 2 = 43.5.

So half of the building measures 43.5 square feet.

Well explained 👍

Problem 3

Calculate √87 x 5.

Okay, lets begin

46.635

Explanation

The first step is to find the square root of 87, which is approximately 9.327.

The second step is to multiply 9.327 by 5. So, 9.327 x 5 ≈ 46.635.

Well explained 👍

Problem 4

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

Okay, lets begin

The square root is 9.

Explanation

To find the square root, we need to find the sum of (81 + 6). 81 + 6 = 87, and then √87 ≈ 9.327.

However, if considering (81 + 6) = 87, and for simplicity, this is just an example setup; the value of √87 is approximately 9.327.

Well explained 👍

Problem 5

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

Okay, lets begin

The perimeter of the rectangle is approximately 94.654 units.

Explanation

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

Perimeter = 2 × (√87 + 38) ≈ 2 × (9.327 + 38) ≈ 2 × 47.327 ≈ 94.654 units.

Well explained 👍

FAQ on Square Root of 87

1.What is √87 in its simplest form?

The prime factorization of 87 is 3 x 29, so the simplest form of √87 remains √87, as it cannot be further simplified to a simpler radical form.

2.Mention the factors of 87.

Factors of 87 are 1, 3, 29, and 87.

3.Calculate the square of 87.

We get the square of 87 by multiplying the number by itself, that is 87 x 87 = 7569.

4.Is 87 a prime number?

5.87 is divisible by?

87 is divisible by 1, 3, 29, and 87.

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.

Fun Fact

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