115 LearnersLast updated on May 26th, 2025
Square Root of 293
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 293.
What is the Square Root of 293?
The square root is the inverse of the square of the number. 293 is not a perfect square. The square root of 293 is expressed in both radical and exponential form. In the radical form, it is expressed as √293, whereas (293)^(1/2) in the exponential form. √293 ≈ 17.11724, 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 293
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 and approximation methods are used. Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 293 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 293 is broken down into its prime factors.
Step 1: Finding the prime factors of 293 293 is a prime number itself. Thus, its prime factorization is simply 293.
Step 2: Since 293 is a prime number and not a perfect square, calculating its square root using prime factorization is not feasible.
Square Root of 293 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 293, we need to group it as 93 and 2.
Step 2: Now we need to find n whose square is less than or equal to 2. We can say n as ‘1’ because 1 × 1 is lesser than or equal to 2. Now the quotient is 1 after subtracting 2 - 1, the remainder is 1.
Step 3: Now let us bring down 93, which is the new dividend. Add the old divisor with the same number 1 + 1 we get 2, which will be our new divisor.
Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 2n as the new divisor, we need to find the value of n.
Step 5: The next step is finding 2n × n ≤ 193. Let us consider n as 7; now 27 × 7 = 189.
Step 6: Subtract 193 from 189, the difference is 4, and the quotient is 17.
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 400.
Step 8: Now we need to find the new divisor, which is 34, because 341 × 1 = 341.
Step 9: Subtracting 341 from 400, we get the result 59.
Step 10: Now the quotient is 17.1.
Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values, continue until the remainder is zero.
So the square root of √293 is approximately 17.11.
Square Root of 293 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 293 using the approximation method.
Step 1: Now we have to find the closest perfect square of √293. The smallest perfect square less than 293 is 289, and the largest perfect square greater than 293 is 324. √293 falls somewhere between 17 and 18.
Step 2: Now we need to apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Going by the formula (293 - 289) ÷ (324 - 289) = 4 / 35 ≈ 0.114. 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 17 + 0.114 ≈ 17.114. So the square root of 293 is approximately 17.114.
Common Mistakes and How to Avoid Them in the Square Root of 293
Students do make mistakes while finding the square root, like 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 keep away from 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 either happen in subtracting or elsewhere.
Square Root of 293 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √293?
The area of the square is approximately 293 square units.
Explanation
The area of the square = side².
The side length is given as √293.
Area of the square = side² = √293 × √293 = 293.
Therefore, the area of the square box is approximately 293 square units.
Problem 2
A square-shaped building measuring 293 square feet is built; if each of the sides is √293, what will be the square feet of half of the building?
146.5 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 293 by 2, we get 146.5.
So half of the building measures 146.5 square feet.
Problem 3
Calculate √293 × 5.
Approximately 85.586
Explanation
The first step is to find the square root of 293, which is approximately 17.11724.
The second step is to multiply 17.11724 by 5.
So 17.11724 × 5 ≈ 85.586.
Problem 4
What will be the square root of (289 + 4)?
The square root is approximately 17.117
Explanation
To find the square root, we need to find the sum of (289 + 4). 289 + 4 = 293, and then √293 ≈ 17.117.
Therefore, the square root of (289 + 4) is approximately ±17.117.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √293 units and the width ‘w’ is 38 units.
We find the perimeter of the rectangle as approximately 110.234 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√293 + 38) = 2 × (17.117 + 38) = 2 × 55.117 ≈ 110.234 units.
FAQ on Square Root of 293
1.What is √293 in its simplest form?
2.Is 293 a prime number?
3.Calculate the square of 293.
4.How is the approximation method useful for finding square roots?
5.Is the square root of 293 rational or irrational?
6.How does learning Algebra help students in India make better decisions in daily life?
7.How can cultural or local activities in India support learning Algebra topics such as Square Root of 293?
8.How do technology and digital tools in India support learning Algebra and Square Root of 293?
9.Does learning Algebra support future career opportunities for students in India?
Important Glossaries for the Square Root of 293
- 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 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.
- Prime number: A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. Examples include 2, 3, 5, 7, 11, 13, etc.
- Approximation method: A method used to estimate the value of a square root by comparing it to nearby perfect squares and using interpolation.
- Long division method: A step-by-step technique to determine the square root of a number by dividing it into manageable parts, typically used for non-perfect squares.
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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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