117 LearnersLast updated on May 26th, 2025
Square Root of 703
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 the field of vehicle design, finance, etc. Here, we will discuss the square root of 703.
What is the Square Root of 703?
The square root is the inverse of the square of the number. 703 is not a perfect square. The square root of 703 is expressed in both radical and exponential forms. In the radical form, it is expressed as √703, whereas (703)^(1/2) in the exponential form. √703 ≈ 26.5141, 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 703
The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where 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 703 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 703 is broken down into its prime factors.
Step 1: Finding the prime factors of 703. Breaking it down, we get 19 × 37: 19^1 × 37^1.
Step 2: Now we found out the prime factors of 703. The second step is to make pairs of those prime factors. Since 703 is not a perfect square, the digits of the number can’t be grouped in pairs. Therefore, calculating 703 using prime factorization is impossible.
Square Root of 703 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 703, we need to group it as 03 and 7.
Step 2: Now we need to find n whose square is less than or equal to 7. We can say n as ‘2’ because 2 × 2 = 4 is lesser than 7. Now the quotient is 2, and after subtracting 4 from 7, the remainder is 3.
Step 3: Bring down 03, making it 303, which is the new dividend. Add the old divisor with the same number, 2 + 2 = 4, which will be our new divisor.
Step 4: The new divisor will be 4n. We need to find the value of n such that 4n × n is less than or equal to 303. Let's consider n as 6, then 46 × 6 = 276.
Step 5: Subtract 276 from 303, and the difference is 27, and the quotient is 26.
Step 6: 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 2700.
Step 7: Now we need to find the new divisor, which will be 532 because 532 × 5 = 2660.
Step 8: Subtracting 2660 from 2700, we get 40.
Step 9: Continue doing these steps until we get two numbers after the decimal point.
So the approximate square root of √703 ≈ 26.5141.
Square Root of 703 by Approximation Method
Approximation method is another method for finding the 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 703 using the approximation method.
Step 1: Now we have to find the closest perfect square of √703. The smallest perfect square less than 703 is 676, and the largest perfect square greater than 703 is 729. √703 falls somewhere between 26 and 27.
Step 2: Now we need to apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula: (703 - 676) / (729 - 676) = 27/53 ≈ 0.509. Adding the integer part, 26, to the decimal, 0.509, we get 26.509. Thus, the square root of 703 is approximately 26.509.
Common Mistakes and How to Avoid Them in the Square Root of 703
Students often make mistakes while finding the square root, such as forgetting about the negative square root, skipping long division methods, etc. 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 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 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 a 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 is wrong, 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. This may either happen in subtracting or elsewhere.
Square root of 703 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √703?
The area of the square is approximately 703 square units.
Explanation
The area of the square = side².
The side length is given as √703.
Area of the square = side² = √703 × √703 = 703.
Therefore, the area of the square box is approximately 703 square units.
Problem 2
A square-shaped building measuring 703 square feet is built; if each of the sides is √703, what will be the square feet of half of the building?
351.5 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped
. Dividing 703 by 2 = we get 351.5.
So half of the building measures 351.5 square feet.
Problem 3
Calculate √703 × 5.
Approximately 132.57
Explanation
The first step is to find the square root of 703, which is approximately 26.5141.
The second step is to multiply 26.5141 by 5.
So 26.5141 × 5 ≈ 132.57.
Problem 4
What will be the square root of (703 + 25)?
The square root is 28.
Explanation
To find the square root, we need to find the sum of (703 + 25). 703 + 25 = 728, and then √728 ≈ 27.
Therefore, the square root of (703 + 25) is approximately 27.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √703 units and the width ‘w’ is 38 units.
We find the perimeter of the rectangle as approximately 129.03 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√703 + 38) = 2 × (26.5141 + 38) = 2 × 64.5141 ≈ 129.03 units.
FAQ on Square Root of 703
1.What is √703 in its simplest form?
2.Mention the factors of 703.
3.Calculate the square of 703.
4.Is 703 a prime number?
5.703 is divisible by?
6.How does learning Algebra help students in Qatar make better decisions in daily life?
7.How can cultural or local activities in Qatar support learning Algebra topics such as Square Root of 703?
8.How do technology and digital tools in Qatar support learning Algebra and Square Root of 703?
9.Does learning Algebra support future career opportunities for students in Qatar?
Important Glossaries for the Square Root of 703
- Square root: A square root is the inverse of a square. Example: 4² = 16, and the inverse of the square is the square root, that is √16 = 4.
- Irrational number: An irrational number 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, it is always the positive square root that is more commonly used due to its relevance in real-world applications. That is the reason it is also known as the principal square root.
- 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 4².
- Prime factorization: Prime factorization is the process of expressing a number as the product of its prime numbers.
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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
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