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Last updated on May 26th, 2025

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Square Root of 870

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If a number is multiplied by itself, the result is a square. The inverse of a 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 870.

Square Root of 870 for Canadian Students
Professor Greenline from BrightChamps

What is the Square Root of 870?

The square root is the inverse of the square of a number. 870 is not a perfect square. The square root of 870 is expressed in both radical and exponential form. In the radical form, it is expressed as √870, whereas (870)^(1/2) in the exponential form. √870 ≈ 29.4958, 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 870

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
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Square Root of 870 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 870 is broken down into its prime factors:

 

Step 1: Finding the prime factors of 870

 

Breaking it down, we get 2 x 3 x 5 x 29: 2^1 x 3^1 x 5^1 x 29^1

 

Step 2: Now we have found the prime factors of 870. The second step is to make pairs of those prime factors. Since 870 is not a perfect square, the digits of the number can’t be grouped in pairs. Therefore, calculating √870 using prime factorization alone is not straightforward.

Professor Greenline from BrightChamps

Square Root of 870 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, group the numbers from right to left. In the case of 870, we need to group it as 70 and 8.

 

Step 2: Now we need to find a number whose square is less than or equal to 8. We can say this number is 2, as 2 x 2 = 4. The quotient is 2, and the remainder is 8 - 4 = 4.

 

Step 3: Bring down 70, which is the new dividend. Add the old divisor with the same number: 2 + 2 = 4, which will be our new divisor.

 

Step 4: Find a digit n such that 4n x n is less than or equal to 470. Let n be 9, then 49 x 9 = 441.

 

Step 5: Subtract 441 from 470, the difference is 29, and the quotient becomes 29.

 

Step 6: Since the dividend is less than the divisor, add a decimal point. Now add two zeroes to the dividend, making it 2900.

 

Step 7: Find the new divisor, which is 298, as 298 x 9 = 2682.

 

Step 8: Subtract 2682 from 2900 to get a result of 218.

 

Step 9: The process continues, and the quotient is approximately 29.49.

 

So, the square root of √870 is approximately 29.4958.

Professor Greenline from BrightChamps

Square Root of 870 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's learn how to find the square root of 870 using the approximation method.

 

Step 1: Find the closest perfect square of √870. The smallest perfect square less than 870 is 841, and the largest perfect square greater than 870 is 900. √870 falls somewhere between 29 and 30.

 

Step 2: Apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square).

 

Using the formula: (870 - 841) / (900 - 841) = 29/59 ≈ 0.49. Adding this to 29, the square root of 870 is approximately 29.49.

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Common Mistakes and How to Avoid Them in the Square Root of 870

Students often make mistakes while finding square roots, such as forgetting about the negative square root or skipping steps in long division. Let's look at a few common mistakes in detail.

Mistake 1

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Forgetting about the negative square root

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It is important to remember that a number has both positive and negative square roots. However, we typically focus on the positive square root for practical purposes.

For example: √50 = 7.07, but there is also -7.07, which should not be ignored in theoretical contexts.

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Square Root of 870 Examples

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Max, the Girl Character from BrightChamps

Problem 1

Can you help Max find the area of a square box if its side length is given as √870?

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The area of the square is approximately 756.05 square units.

Explanation

The area of the square = side^2.

The side length is given as √870.

Area of the square = side^2 = (√870) x (√870) = 870.

Therefore, the area of the square box is approximately 870 square units.

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Max, the Girl Character from BrightChamps

Problem 2

A square-shaped building measuring 870 square feet is built; if each of the sides is √870, what will be the square feet of half of the building?

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435 square feet

Explanation

Divide the given area by 2 as the building is square-shaped.

Dividing 870 by 2 = 435.

So half of the building measures 435 square feet.

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Max, the Girl Character from BrightChamps

Problem 3

Calculate √870 x 5.

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Approximately 147.48

Explanation

First, find the square root of 870, which is approximately 29.4958.

Then multiply 29.4958 by 5.

So, 29.4958 x 5 ≈ 147.48.

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Max, the Girl Character from BrightChamps

Problem 4

What will be the square root of (870 + 30)?

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The square root is approximately 30.

Explanation

To find the square root, first find the sum of (870 + 30). 870 + 30 = 900, and the square root of 900 is ±30.

Therefore, the square root of (870 + 30) is ±30.

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Max, the Girl Character from BrightChamps

Problem 5

Find the perimeter of a rectangle if its length ‘l’ is √870 units and the width ‘w’ is 30 units.

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The perimeter of the rectangle is approximately 118.99 units.

Explanation

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

Perimeter = 2 × (√870 + 30) ≈ 2 × (29.4958 + 30) ≈ 2 × 59.4958 ≈ 118.99 units.

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FAQ on Square Root of 870

1.What is √870 in its simplest form?

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2.Mention the factors of 870.

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3.Calculate the square of 870.

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4.Is 870 a prime number?

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5.870 is divisible by?

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6.How does learning Algebra help students in Canada make better decisions in daily life?

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7.How can cultural or local activities in Canada support learning Algebra topics such as Square Root of 870?

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8.How do technology and digital tools in Canada support learning Algebra and Square Root of 870?

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9.Does learning Algebra support future career opportunities for students in Canada?

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Professor Greenline from BrightChamps

Important Glossaries for the Square Root of 870

  • Square root: A square root is the inverse of a square. Example: 4^2 = 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.
     
  • Perfect square: A perfect square is a number that is the square of an integer. For example, 16 is a perfect square because it equals 4^2.
     
  • Decimal: If a number has a whole number and a fraction in a single number, then it is called a decimal. For example, 7.86, 8.65, and 9.42 are decimals.
     
  • Prime factorization: Prime factorization is the process of expressing a number as the product of its prime factors. For example, the prime factorization of 28 is 2 x 2 x 7.
Professor Greenline from BrightChamps

About BrightChamps in Canada

At BrightChamps, we know algebra is more than just symbols—it’s a key to open many doors! Our aim is to support kids across Canada in grasping important math skills, such as today’s focus on the Square Root of 870, highlighting square roots in a fun, engaging, and easy-to-understand way. Whether your child is measuring how fast a roller coaster moves at Canada’s Wonderland, tracking hockey scores, or planning their allowance for the latest gadgets, mastering algebra helps build their confidence for daily tasks. Our hands-on lessons make learning enjoyable and straightforward. Since kids in Canada learn in diverse ways, we tailor lessons to their individual style. From Toronto’s busy streets to British Columbia’s stunning landscapes, BrightChamps brings math to life across Canada. Let’s make square roots a fun part of your child’s math experience!
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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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Max, the Girl Character from BrightChamps

Fun Fact

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

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