127 LearnersLast updated on May 26th, 2025
Square Root of 1087
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 like vehicle design, finance, etc. Here, we will discuss the square root of 1087.
What is the Square Root of 1087?
The square root is the inverse of the square of the number. 1087 is not a perfect square. The square root of 1087 is expressed in both radical and exponential form. In the radical form, it is expressed as √1087, whereas (1087)^(1/2) in the exponential form. √1087 ≈ 32.961, 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 1087
The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where 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 1087 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 1087 is broken down into its prime factors.
Step 1: Finding the prime factors of 1087 Breaking it down, we find that 1087 is a prime number, so its only factors are 1 and 1087.
Step 2: Since 1087 is a prime number, calculating the square root using prime factorization directly is not possible.
Square Root of 1087 by Long Division Method
The long division method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square number 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, we need to group the numbers from right to left. In the case of 1087, we need to group it as 87 and 10.
Step 2: Now we need to find n whose square is ≤ 10. We can say n as ‘3’ because 3^2 = 9 is lesser than or equal to 10. Now the quotient is 3 and after subtracting 10 - 9, the remainder is 1.
Step 3: Now let us bring down 87 which is the new dividend. Add the old divisor with the same number 3 + 3 = 6, which will be our new divisor.
Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 6n as the new divisor, we need to find the value of n.
Step 5: The next step is finding 6n × n ≤ 187. Let us consider n as 3, now 63 × 3 = 189, which is too high, so we try n = 2, now 62 × 2 = 124.
Step 6: Subtract 187 from 124, the difference is 63, and the quotient is 32.
Step 7: Since the remainder is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 6300.
Step 8: Find the new divisor which is 649 because 6490 × 9 = 5841.
Step 9: Subtracting 5841 from 6300, we get the result 459.
Step 10: Now the quotient is 32.9
Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values, continue until the remainder is zero.
So the square root of √1087 ≈ 32.96
Square Root of 1087 by Approximation Method
The approximation method is another method for finding 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 1087 using the approximation method.
Step 1: Now we have to find the closest perfect squares of √1087. The smallest perfect square less than 1087 is 1024, and the largest perfect square greater than 1087 is 1089. √1087 falls somewhere between 32 and 33.
Step 2: Now we need to apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square) Using the formula (1087 - 1024) ÷ (1089 - 1024) = 0.963 Using the formula, we identified the decimal point of our square root. The next step is adding the value we got initially to the decimal number, which is 32 + 0.963 = 32.963.
So the square root of 1087 is approximately 32.963.
Common Mistakes and How to Avoid Them in the Square Root of 1087
Students do make mistakes while finding the square root, like forgetting about the negative square root or skipping long division steps, etc. Now let us look at a few of those mistakes that students tend to make in detail.
Mistake 1
Forgetting about the negative square root
It is important to make students aware that a number does have both positive and negative square roots. However, we will be taking only the positive square root, as it is the required one.
For example: √50 ≈ 7.07, there is also -7.07 which should not be forgotten.
Mistake 2
Not adding square root symbol in proper places
Not using the square root properly is another mistake that children make. To resolve this, we need to teach children that simplifying the numbers inside the square root is important and then move on to the second step.
For example: √(12 + 24) ≠ √12 + √24. The right way is √(12 + 24) = √36.
Mistake 3
Not finding the correct value of a non-perfect square
The first step that needs to be taught to children is to simplify the numbers inside the square root. This is important so that students do not make mistakes while identifying the approximate value.
For example: √50 ≈ 7 is incorrect; the correct answer is √50 ≈ 7.071.
Mistake 4
Confusing the square root symbol with the cube root
Students need to be taught the difference between cube root and square root constantly as this will help them avoid mistakes.
For example: √50 and ∛50 are different.
Mistake 5
Making mistakes in long division
Finding a square root using the long division method involves many steps. Due to this, many students might skip a step accidentally, which results in a wrong answer at the end of the sum. This may either happen in subtracting or elsewhere.
Square root of 1087 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √1087?
The area of the square is approximately 1087 square units.
Explanation
The area of the square = side^2. The side length is given as √1087. Area of the square = side^2 = √1087 × √1087 = 1087. Therefore, the area of the square box is approximately 1087 square units.
Problem 2
A square-shaped floor measuring 1087 square feet is built; if each of the sides is √1087, what will be the square feet of half of the floor?
543.5 square feet
Explanation
We can just divide the given area by 2 as the floor is square-shaped.
Dividing 1087 by 2 = we get 543.5
So half of the floor measures 543.5 square feet.
Problem 3
Calculate √1087 × 5.
Approximately 164.805
Explanation
The first step is to find the square root of 1087, which is approximately 32.96.
The second step is to multiply 32.96 by 5.
So 32.96 × 5 ≈ 164.805
Problem 4
What will be the square root of (1000 + 87)?
The square root is approximately 33.
Explanation
To find the square root, we need to find the sum of (1000 + 87).
1000 + 87 = 1087, and then the square root of 1087 is approximately 32.96.
Therefore, the square root of (1000 + 87) is approximately ±32.96.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √1087 units and the width ‘w’ is 50 units.
We find the perimeter of the rectangle as approximately 165.92 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√1087 + 50)
= 2 × (32.96 + 50)
= 2 × 82.96
= 165.92 units.
FAQ on Square Root of 1087
1.What is √1087 in its simplest form?
2.Mention the factors of 1087.
3.Calculate the square of 1087.
4.Is 1087 a prime number?
5.1087 is divisible by?
6.How does learning Algebra help students in Singapore make better decisions in daily life?
7.How can cultural or local activities in Singapore support learning Algebra topics such as Square Root of 1087?
8.How do technology and digital tools in Singapore support learning Algebra and Square Root of 1087?
9.Does learning Algebra support future career opportunities for students in Singapore?
Important Glossaries for the Square Root of 1087
- Square root: A square root is the inverse of squaring a number. For example, 4^2 = 16 and the inverse of the square is the square root, which is √16 = 4.
- Irrational number: An irrational number is a number that cannot be written as a simple fraction, i.e., in the form p/q, where q is not equal to zero and p and q are integers.
- Prime Number: A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers.
- Long Division: A method used in mathematics to find the square root of non-perfect square numbers through a series of steps involving division and subtraction.
- Approximation: The process of finding a value that is close enough to the right answer, usually with some thought or calculation involved.
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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.
