123 LearnersLast updated on May 26th, 2025
Square Root of 853
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 engineering, finance, etc. Here, we will discuss the square root of 853.
What is the Square Root of 853?
The square root is the inverse of squaring a number. 853 is not a perfect square. The square root of 853 is expressed in both radical and exponential form. In the radical form, it is expressed as √853, whereas (853)^(1/2) in the exponential form. √853 ≈ 29.207, 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 853
The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers like 853, 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 853 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 853 is broken down into its prime factors.
Step 1: Finding the prime factors of 853 853 is a prime number, and thus it cannot be broken down into smaller prime factors. Since 853 is not a perfect square, calculating √853 using prime factorization is not possible.
Square Root of 853 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, group the numbers from right to left. In the case of 853, we group it as 53 and 8.
Step 2: Now, find n whose square is less than or equal to 8. We select n as 2 because 2 x 2 = 4, which is less than 8. Now the quotient is 2, and subtracting 4 from 8 leaves a remainder of 4.
Step 3: Bring down 53, making the new dividend 453. Add the old divisor with the same number: 2 + 2 = 4.
Step 4: The new divisor will be 2n. We need to find the value of n.
Step 5: The next step is finding 2n x n ≤ 453. Let us consider n as 9, now 49 x 9 = 441.
Step 6: Subtract 441 from 453, leaving a remainder of 12, and the quotient is 29.
Step 7: Since the dividend 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 1200.
Step 8: Find the new divisor, which is 58, because 582 x 2 = 1164.
Step 9: Subtracting 1164 from 1200 gives a result of 36.
Step 10: The quotient is 29.2.
Step 11: Continue these steps until we achieve the desired precision.
So the square root of √853 is approximately 29.207.
Square Root of 853 by Approximation Method
The approximation method is another way to find square roots. It is an easy method to approximate the square root of a given number. Now let us learn how to find the square root of 853 using the approximation method.
Step 1: Find the closest perfect squares around √853. The smallest perfect square less than 853 is 841, and the largest perfect square greater than 853 is 900. √853 falls somewhere between 29 and 30.
Step 2: Apply the formula: (Given number - smaller perfect square) / (Greater perfect square - smaller perfect square).
Using the formula: (853 - 841) / (900 - 841) = 12 / 59 ≈ 0.203. Adding the initial whole number to the decimal: 29 + 0.203 = 29.203, so the square root of 853 is approximately 29.203.
Common Mistakes and How to Avoid Them in the Square Root of 853
Students make mistakes while finding square roots, such as forgetting about the negative square root or skipping steps in methods. Let us look at a few common mistakes and how to avoid them.
Mistake 1
Forgetting about the negative square root
It is essential to make students aware that a number has both positive and negative square roots. However, we typically consider only the positive square root as it is more commonly used.
For example: √50 = ±7.07, but often only the positive root is used.
Mistake 2
Not adding the square root symbol in proper places
Incorrect usage of the square root symbol is another mistake. It's important to properly simplify inside the square root before proceeding.
For example: √(12+24) ≠ √12 + √24; the correct method is √(12+24) = √36 = 6.
Mistake 3
Not finding the correct value of a non-perfect square
Students should be taught to simplify numbers inside the square root to avoid mistakes in identifying approximate values.
For example: √50 ≈ 7.071067, not 7.
Mistake 4
Confusing the square root symbol with the cube root
Teach the difference between cube root and square root consistently.
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. Students may skip a step accidentally, leading to incorrect results. This may happen in subtraction or other steps.
Square Root of 853 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √853?
The area of the square is approximately 727.809 square units.
Explanation
The area of the square = side^2.
The side length is given as √853.
Area of the square = (√853)^2 = 29.207 x 29.207 ≈ 853.
Therefore, the area of the square box is approximately 853 square units.
Problem 2
A square-shaped field measuring 853 square meters is built; if each of the sides is √853, what will be the square meters of half of the field?
426.5 square meters
Explanation
Divide the given area by 2 as the field is square-shaped.
Dividing 853 by 2, we get 426.5.
So half of the field measures 426.5 square meters.
Problem 3
Calculate √853 x 5.
Approximately 146.035
Explanation
First, find the square root of 853, which is approximately 29.207.
Then multiply 29.207 by 5. So 29.207 x 5 ≈ 146.035.
Problem 4
What will be the square root of (853 + 47)?
The square root is 30.
Explanation
To find the square root, calculate the sum of (853 + 47). 853 + 47 = 900, and the square root of 900 is 30.
Therefore, the square root of (853 + 47) is 30.
Problem 5
Find the perimeter of a rectangle if its length ‘l’ is √853 units and the width ‘w’ is 47 units.
The perimeter of the rectangle is approximately 152.414 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√853 + 47) = 2 × (29.207 + 47) = 2 × 76.207 ≈ 152.414 units.
FAQ on Square Root of 853
1.What is √853 in its simplest form?
2.Mention the factors of 853.
3.Calculate the square of 853.
4.Is 853 a prime number?
5.853 is divisible by?
6.How does learning Algebra help students in Canada make better decisions in daily life?
7.How can cultural or local activities in Canada support learning Algebra topics such as Square Root of 853?
8.How do technology and digital tools in Canada support learning Algebra and Square Root of 853?
9.Does learning Algebra support future career opportunities for students in Canada?
Important Glossaries for the Square Root of 853
- Square root: A square root is the inverse of squaring a number. 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.
- Prime number: A prime number is a number greater than 1 with no divisors other than 1 and itself.
- Decimal: If a number has a whole number and a fraction in a single number, it is called a decimal. For example: 7.86, 8.65, and 9.42 are decimals.
- Perfect square: A perfect square is an integer that is the square of an integer. For example, 16 is a perfect square because it is 4^2.
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Jaskaran Singh Saluja
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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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