119 LearnersLast updated on May 26th, 2025
Square Root of 732
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 732.
What is the Square Root of 732?
The square root is the inverse of the square of the number. 732 is not a perfect square. The square root of 732 is expressed in both radical and exponential form. In the radical form, it is expressed as √732, whereas in the exponential form as (732)^(1/2). √732 ≈ 27.0555, 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 732
The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers like 732, 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 732 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 732 is broken down into its prime factors:
Step 1: Finding the prime factors of 732
Breaking it down, we get 2 × 2 × 3 × 61: 2^2 × 3 × 61
Step 2: Now we have found the prime factors of 732. The next step is to make pairs of those prime factors. Since 732 is not a perfect square, the digits of the number can’t be grouped in pairs to find an exact square root. Therefore, calculating √732 using prime factorization alone is not feasible.
Square Root of 732 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 732, we need to group it as 32 and 7.
Step 2: Now we need to find n whose square is ≤ 7. We can say n is '2' because 2 × 2 = 4, which is less than 7. Now the quotient is 2, and after subtracting 4 from 7, the remainder is 3.
Step 3: Bring down 32, making the new dividend 332. Add the old divisor with the same number 2 + 2 to get 4, which will be our new divisor.
Step 4: The new divisor will be the sum of the quotient and twice the previous quotient. We get 4n as the new divisor. We need to find the value of n such that 4n × n ≤ 332.
Step 5: Consider n as 8, now 48 × 8 = 384, which is less than 332. We need to try a smaller number.
Step 6: Trying n as 7, 47 × 7 = 329, which fits. So we subtract 329 from 332, leaving a remainder of 3, and the quotient is 27.
Step 7: Since the dividend is less than the divisor, we add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend, making it 300.
Step 8: Now find the new divisor, which is 540 because 540 × 0.5 = 270, which is less than 300.
Step 9: Subtracting 270 from 300 gives a remainder of 30.
Step 10: Continue these steps until we get two numbers after the decimal point. If there is no remainder, continue until the remainder is zero.
So the square root of √732 ≈ 27.0555.
Square Root of 732 by Approximation Method
The approximation method is an easy way to find the square root of a given number. Now let us learn how to find the square root of 732 using the approximation method.
Step 1: Find the closest perfect squares to √732. The smallest perfect square less than 732 is 729, and the largest perfect square greater than 732 is 784. √732 falls between 27 and 28.
Step 2: Now apply the formula: (Given number - smallest perfect square) ÷ (Greater perfect square - smallest perfect square). Using the formula (732 - 729) ÷ (784 - 729) = 3 ÷ 55 ≈ 0.055 Add the value obtained to the lower bound: 27 + 0.055 ≈ 27.055.
So the square root of 732 is approximately 27.055.
Common Mistakes and How to Avoid Them in the Square Root of 732
Students often make mistakes while finding square roots, such as forgetting about the negative square root or skipping long division methods. Let us look at a few mistakes students tend to make in detail.
Mistake 1
Forgetting about the negative square root
It is important to remind students that a number has both positive and negative square roots. However, we typically consider only the positive square root unless specified otherwise.
For example: √50 = 7.07, but there is also -7.07.
Mistake 2
Not adding the square root symbol in proper places
Incorrect use of the square root symbol is another common mistake. Students must learn to simplify the numbers inside the square root before proceeding.
For example, √(12+24) ≠ √12 + √24.
The correct simplification is √(12+24) = √36.
Mistake 3
Not finding the correct value of a non-perfect square
The first step is to simplify the numbers inside the square root to avoid mistakes in identifying the approximate value.
For example, if √50 = 7 is wrong, the correct value is √50 ≈ 7.071.
Mistake 4
Confusing the square root symbol with the cube root
Students need to understand the difference between cube root and square root to avoid confusion.
For example, √50 and ∛50 are different.
Mistake 5
Making mistakes in long division
Finding a square root using the long division method involves multiple steps. Students may skip a step accidentally, resulting in incorrect answers. This can occur during subtraction or elsewhere in the process.
Square Root of 732 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √732?
The area of the square is approximately 536.71 square units.
Explanation
The area of the square = side².
The side length is given as √732.
Area of the square = side² = √732 × √732 ≈ 27.055 × 27.055 ≈ 732.
Therefore, the area of the square box is approximately 732 square units.
Problem 2
A square-shaped garden measuring 732 square feet is built. If each of the sides is √732, what will be the square feet of half of the garden?
366 square feet
Explanation
We can divide the given area by 2 since the garden is square-shaped.
Dividing 732 by 2 gives 366.
So half of the garden measures 366 square feet.
Problem 3
Calculate √732 × 5.
Approximately 135.28
Explanation
The first step is to find the square root of 732, which is approximately 27.055.
The second step is to multiply 27.055 by 5.
So 27.055 × 5 ≈ 135.28.
Problem 4
What will be the square root of (732 + 6)?
Approximately 27.495
Explanation
To find the square root, we need to find the sum of (732 + 6). 732 + 6 = 738, and then the square root of 738 is approximately 27.495.
Therefore, the square root of (732 + 6) is approximately ±27.495.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √732 units and the width ‘w’ is 38 units.
The perimeter of the rectangle is approximately 130.11 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√732 + 38) ≈ 2 × (27.055 + 38) ≈ 2 × 65.055 ≈ 130.11 units.
FAQ on Square Root of 732
1.What is √732 in its simplest form?
2.Mention the factors of 732.
3.Calculate the square of 732.
4.Is 732 a prime number?
5.732 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 732?
8.How do technology and digital tools in Singapore support learning Algebra and Square Root of 732?
9.Does learning Algebra support future career opportunities for students in Singapore?
Important Glossaries for the Square Root of 732
- Square root: A square root is the inverse of a square. For example, 5² = 25 and the inverse of the square is the square root, which is √25 = 5.
- 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, 144 is a perfect square since it is 12².
- Long division method: A method used to find the square root of numbers, especially when they are not perfect squares, through systematic division.
- Approximation method: A technique used to estimate the square root of a number by comparing it to the nearest perfect squares and using interpolation.
Explore More algebra
About BrightChamps in Singapore
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.
