163 LearnersLast updated on May 26th, 2025
Square Root of 1762
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, and more. Here, we will discuss the square root of 1762.
What is the Square Root of 1762?
The square root is the inverse of the square of a number. 1762 is not a perfect square. The square root of 1762 is expressed in both radical and exponential form. In radical form, it is expressed as √1762, whereas in exponential form it is expressed as (1762)^(1/2). √1762 ≈ 41.9845, 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 1762
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:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 1762 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 1762 is broken down into its prime factors.
Step 1: Finding the prime factors of 1762. Breaking it down, we get 2 × 881.
Step 2: Now we found out the prime factors of 1762. The second step is to make pairs of those prime factors. Since 1762 is not a perfect square, the digits of the number can’t be grouped in pairs.
Therefore, calculating 1762 using prime factorization is not straightforward.
Square Root of 1762 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, we need to group the numbers from right to left. In the case of 1762, we need to group it as 62 and 17.
Step 2: Now we need to find n whose square is ≤ 17. We can say n is ‘4’ because 4 × 4 = 16, which is less than or equal to 17. Now the quotient is 4. After subtracting 16 from 17, the remainder is 1.
Step 3: Now let us bring down 62, which is the new dividend. Add the old divisor with the same number 4 + 4, we get 8, which will be our new divisor.
Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 8n as the new divisor; we need to find the value of n.
Step 5: The next step is finding 8n × n ≤ 162. Let us consider n as 2, now 82 × 2 = 164, which is too large. Let's try n = 1, so 81 × 1 = 81.
Step 6: Subtract 81 from 162, the difference is 81, and the quotient is 41.
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 8100.
Step 8: Now we need to find the new divisor that is 829 because 829 × 9 = 7461.
Step 9: Subtracting 7461 from 8100, we get the result 639.
Step 10: Now the quotient is 41.9.
Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values, continue till the remainder is zero.
So the square root of √1762 is approximately 41.98.
Square Root of 1762 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 1762 using the approximation method.
Step 1: Now we have to find the closest perfect squares of √1762. The smallest perfect square below 1762 is 1681, and the largest perfect square above 1762 is 1849. √1762 falls somewhere between 41 and 43.
Step 2: Now we need to apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square).
Using the formula: (1762 - 1681) ÷ (1849 - 1681) = 81 ÷ 168 ≈ 0.482.
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 41 + 0.48 = 41.48.
So the square root of 1762 is approximately 41.48.
Common Mistakes and How to Avoid Them in the Square Root of 1762
Students make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in the long division method. Now let us look at a few of those mistakes in detail.
Mistake 1
Forgetting about the negative square root
It is important to make students aware that a number has 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 the 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 is the wrong method of using roots.
The right way of using roots 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 ≈ 7.071, not 7.
Mistake 4
Confusing the square root symbol with the cube root
Students need to be taught the difference between the 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 calculation. This may happen in subtraction or elsewhere.
Square Root of 1762 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √1762?
The area of the square is 3104.1 square units.
Explanation
The area of the square = side^2.
The side length is given as √1762.
Area of the square = side^2 = √1762 × √1762 ≈ 41.98 × 41.98 ≈ 1762.
Therefore, the area of the square box is approximately 3104.1 square units.
Problem 2
A square-shaped building measuring 1762 square feet is built; if each of the sides is √1762, what will be the square feet of half of the building?
881 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 1762 by 2, we get 881.
So half of the building measures 881 square feet.
Problem 3
Calculate √1762 × 5.
209.92
Explanation
The first step is to find the square root of 1762, which is approximately 41.98.
The second step is to multiply 41.98 by 5. So 41.98 × 5 ≈ 209.92.
Problem 4
What will be the square root of (1762 + 6)?
The square root is approximately 42.05.
Explanation
To find the square root, we need to find the sum of (1762 + 6). 1762 + 6 = 1768, and then √1768 ≈ 42.05.
Therefore, the square root of (1762 + 6) is approximately ±42.05.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √1762 units and the width ‘w’ is 38 units.
We find the perimeter of the rectangle as 159.96 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√1762 + 38) ≈ 2 × (41.98 + 38) ≈ 2 × 79.98 ≈ 159.96 units.
FAQ on Square Root of 1762
1.What is √1762 in its simplest form?
2.Mention the factors of 1762.
3.Calculate the square of 1762.
4.Is 1762 a prime number?
5.1762 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 1762?
8.How do technology and digital tools in Canada support learning Algebra and Square Root of 1762?
9.Does learning Algebra support future career opportunities for students in Canada?
Important Glossaries for the Square Root of 1762
- 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.
- Principal square root: A number has both positive and negative square roots; however, the positive square root is more commonly used due to its applications in the real world. This is known as the principal square root.
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 1762 is 2 × 881.
- Long division method: A technique used to find the square root of numbers that are not perfect squares by dividing the number step-by-step.
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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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