114 LearnersLast updated on May 26th, 2025
Square Root of 1202
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 1202.
What is the Square Root of 1202?
The square root is the inverse of the square of a number. 1202 is not a perfect square. The square root of 1202 can be expressed in both radical and exponential form. In radical form, it is expressed as √1202, whereas in exponential form, it is expressed as (1202)¹/². √1202 ≈ 34.671, 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 1202
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 1202 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 1202 is broken down into its prime factors.
Step 1: Finding the prime factors of 1202 Breaking it down, we get 2 x 601: 2¹ x 601¹
Step 2: Now we found out the prime factors of 1202. Since 1202 is not a perfect square, we cannot make pairs of the prime factors.
Therefore, calculating √1202 using prime factorization is not practical.
Square Root of 1202 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 1202, we need to group it as 02 and 12.
Step 2: Now we need to find n whose square is less than or equal to 12. We can say n as ‘3’ because 3 x 3 = 9 is less than 12. Now the quotient is 3, and after subtracting 9 from 12, the remainder is 3.
Step 3: Now let us bring down 02, which is the new dividend. Add the old divisor with the same number (3 + 3) to get 6, which will be our new divisor.
Step 4: Now we need to find a digit, say m, such that 6m x m is less than or equal to 302.
Step 5: Let m be 4, then 64 x 4 = 256.
Step 6: Subtract 256 from 302, the difference is 46, and the quotient is 34.
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 4600.
Step 8: Now we need to find the new divisor that is 689 because 689 x 6 = 4134.
Step 9: Subtracting 4134 from 4600, we get the result 466.
Step 10: Now the quotient is 34.6.
Step 11: Continue doing these steps until we get two numbers after the decimal point. If there are no decimal values, continue till the remainder is zero.
So the square root of √1202 is approximately 34.671.
Square Root of 1202 by Approximation Method
The approximation method is another way to find square roots. It is an easy method to estimate the square root of a given number. Now let us learn how to find the square root of 1202 using the approximation method.
Step 1: Find the closest perfect squares around √1202. The smallest perfect square less than 1202 is 1156, and the largest perfect square more than 1202 is 1225. √1202 falls somewhere between 34 and 35.
Step 2: Now apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula (1202 - 1156) / (1225 - 1156) = 46 / 69 ≈ 0.667. Adding this to the lower integer value, 34 + 0.667 = 34.667.
So the square root of 1202 is approximately 34.671.
Common Mistakes and How to Avoid Them in the Square Root of 1202
Students often make mistakes while finding square roots, such as forgetting about the negative square root or skipping steps in the long division method. Let us look at a few common mistakes.
Mistake 1
Forgetting about the negative square root
It is important to remember that a number has both positive and negative square roots. However, we typically use only the positive square root.
For example, √1202 ≈ ±34.671.
Mistake 2
Not adding the square root symbol in proper places
Another common mistake is not using the square root symbol correctly. Always simplify the numbers inside the square root first.
For example, √(100 + 102) is not √100 + √102. The correct approach is √202.
Mistake 3
Not finding the correct value of a non-perfect square
It's crucial to approximate non-perfect squares accurately.
For example, √50 ≈ 7.071, not 7.
Mistake 4
Confusing the square root symbol with the cube root
Students often confuse the square root symbol (√) with the cube root symbol (∛).
For example, √8 is different from ∛8.
Mistake 5
Making mistakes in long division
The long division method involves many steps. Skipping a step can lead to incorrect results. Carefully follow each step to find the correct square root.
Square Root of 1202 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √1202?
The area of the square is approximately 1446.44 square units.
Explanation
The area of a square = side².
The side length is given as √1202.
Area of the square = side² = √1202 x √1202 ≈ 34.671 x 34.671 ≈ 1202.
Therefore, the area of the square box is approximately 1446.44 square units.
Problem 2
A square-shaped building measuring 1202 square feet is built; if each of the sides is √1202, what will be the square feet of half of the building?
601 square feet
Explanation
We can divide the given area by 2, as the building is square-shaped.
Dividing 1202 by 2 = 601
So half of the building measures 601 square feet.
Problem 3
Calculate √1202 x 5.
Approximately 173.355
Explanation
The first step is to find the square root of 1202, which is approximately 34.671.
The second step is to multiply 34.671 by 5.
So 34.671 x 5 ≈ 173.355
Problem 4
What will be the square root of (1200 + 2)?
The square root is approximately 34.671.
Explanation
To find the square root, we need to find the sum of (1200 + 2).
1200 + 2 = 1202, and then √1202 ≈ 34.671.
Therefore, the square root of (1200 + 2) is approximately ±34.671.
Problem 5
Find the perimeter of a rectangle if its length ‘l’ is √1202 units and the width ‘w’ is 38 units.
The perimeter of the rectangle is approximately 145.342 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√1202 + 38)
= 2 × (34.671 + 38)
≈ 2 × 72.671
≈ 145.342 units.
FAQ on Square Root of 1202
1.What is √1202 in its simplest form?
2.Mention the factors of 1202.
3.Calculate the square of 1202.
4.Is 1202 a prime number?
5.1202 is divisible by?
6.How does learning Algebra help students in Australia make better decisions in daily life?
7.How can cultural or local activities in Australia support learning Algebra topics such as Square Root of 1202?
8.How do technology and digital tools in Australia support learning Algebra and Square Root of 1202?
9.Does learning Algebra support future career opportunities for students in Australia?
Important Glossaries for the Square Root of 1202
- Square root: A square root is the inverse of squaring a number. Example: 4² = 16, and the square root of 16 is √16 = 4.
- Irrational number: An irrational number is a number that cannot be expressed as a simple fraction. Its decimal form is non-repeating and non-terminating.
- Principal square root: The positive square root of a number, which is most commonly used in calculations, is called the principal square root.
- Decimal: A decimal is a number that includes a fraction represented in a base-10 numeral system, such as 7.86, 8.65, and 9.42.
- Prime factorization: This is the process of expressing a number as the product of its prime factors, which are the building blocks of the number.
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