127 LearnersLast updated on May 26th, 2025
Square Root of 743
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 such as vehicle design and finance. Here, we will discuss the square root of 743.
What is the Square Root of 743?
The square root is the inverse of the square of the number. 743 is not a perfect square. The square root of 743 is expressed in both radical and exponential form. In the radical form, it is expressed as √743, whereas (743)^(1/2) in the exponential form. √743 ≈ 27.258, 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 743
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 743 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 743 is broken down into its prime factors:
Step 1: Finding the prime factors of 743 743 is a prime number, so it cannot be broken down into smaller prime factors. Therefore, calculating 743 using prime factorization is impossible.
Square Root of 743 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 743, we need to group it as 43 and 7.
Step 2: Now we need to find n whose square is less than or equal to 7. We can say n is ‘2’ because 2 x 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 43 to make the new dividend 343. 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 dividend and quotient. Now we get 4n as the new divisor, and we need to find the value of n.
Step 5: The next step is finding 4n × n ≤ 343. Let us consider n as 8, now 48 x 8 = 384 which is more than 343. So, let's try n as 7, 47 x 7 = 329.
Step 6: Subtract 329 from 343, the difference is 14, and the quotient becomes 27.
Step 7: Since the dividend is less than the new 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 1400.
Step 8: Now we need to find the new divisor which is 547 because 547 x 2 = 1094.
Step 9: Subtracting 1094 from 1400 we get the result 306.
Step 10: Now the quotient is 27.2
Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose there are no decimal values, continue till the remainder is zero.
So the square root of √743 is approximately 27.26.
Square Root of 743 by Approximation Method
The approximation method is another method for finding square roots, and 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 743 using the approximation method.
Step 1: Now we have to find the closest perfect square of √743. The smallest perfect square less than 743 is 729 (27^2) and the largest perfect square greater than 743 is 784 (28^2). √743 falls somewhere between 27 and 28.
Step 2: Now we need to apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula (743 - 729) ÷ (784 - 729) = 0.2545. 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 27 + 0.2545 = 27.2545, so the square root of 743 is approximately 27.2545.
Common Mistakes and How to Avoid Them in the Square Root of 743
Students do make mistakes while finding the square root, such as forgetting about the negative square root or skipping long division methods. Now let us look at a few of those mistakes that students tend to make in detail.
Mistake 1
Forgetting about the negative square root
It is important to make students aware that a number does have both positive and negative square roots. However, we generally use only the positive square root, as it is the required one for most applications.
For example: √50 = 7.07, but 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 before moving on to the next step.
For example: √(12+24) ≠ √12 + √24. The correct way to simplify 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; the correct answer is √50 ≈ 7.071067.
Mistake 4
Confusing the square root symbol with the cube root
Students need to be taught the difference between 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 sum. This may happen either during subtraction or elsewhere.
Square Root of 743 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √743?
The area of the square is approximately 551.29 square units.
Explanation
The area of the square = side².
The side length is given as √743.
Area of the square = side² = √743 x √743 ≈ 27.258 x 27.258 ≈ 743.
Therefore, the area of the square box is approximately 551.29 square units.
Problem 2
A square-shaped garden measuring 743 square feet is built; if each of the sides is √743, what will be the square feet of half of the garden?
371.5 square feet
Explanation
We can just divide the given area by 2 as the garden is square-shaped.
Dividing 743 by 2 gives us 371.5.
So half of the garden measures 371.5 square feet.
Problem 3
Calculate √743 x 3.
Approximately 81.774
Explanation
The first step is to find the square root of 743, which is approximately 27.258. The second step is to multiply 27.258 by 3. So 27.258 x 3 ≈ 81.774.
Problem 4
What will be the square root of (729 + 14)?
The square root is approximately 27.258.
Explanation
To find the square root, we need to find the sum of (729 + 14). 729 + 14 = 743, and then √743 ≈ 27.258.
Therefore, the square root of (729 + 14) is approximately ±27.258.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √743 units and the width ‘w’ is 20 units.
We find the perimeter of the rectangle as approximately 94.516 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√743 + 20) ≈ 2 × (27.258 + 20) ≈ 2 × 47.258 ≈ 94.516 units.
FAQ on Square Root of 743
1.What is √743 in its simplest form?
2.Mention the factors of 743.
3.Calculate the square of 743.
4.Is 743 a prime number?
5.743 is divisible by?
Important Glossaries for the Square Root of 743
- Square root: A square root is the inverse of a square. For example, 4² = 16 and the inverse of the square is the square root, which 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.
- Long division method: A method used to find the square roots of non-perfect squares by dividing the number into groups of digits.
- Approximation method: A method to estimate the square root by finding the closest perfect squares and using a proportion to find a decimal approximation.
- Prime number: A natural number greater than 1 that has no positive divisors other than 1 and itself.
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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.
Fun Fact
: He loves to play the quiz with kids through algebra to make kids love it.
