119 LearnersLast updated on May 26th, 2025
Square Root of 1288
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 1288.
What is the Square Root of 1288?
The square root is the inverse of the square of a number. 1288 is not a perfect square. The square root of 1288 is expressed in both radical and exponential form. In radical form, it is expressed as √1288, whereas 1288^(1/2) in exponential form. √1288 ≈ 35.877, 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 1288
The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers like 1288, 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 1288 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 1288 is broken down into its prime factors.
Step 1: Finding the prime factors of 1288
Breaking it down, we get 2 x 2 x 2 x 7 x 23: 2^3 x 7 x 23
Step 2: Now we have found the prime factors of 1288. The second step is to make pairs of those prime factors. Since 1288 is not a perfect square, the digits of the number can’t be grouped in pairs. Therefore, calculating 1288 using prime factorization alone is incomplete.
Square Root of 1288 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 1288, we need to group it as 28 and 12.
Step 2: Now we need to find n whose square is ≤ 12. We can say n as '3' because 3 x 3 = 9 is lesser than or equal to 12. Now the quotient is 3, and after subtracting 9 from 12, the remainder is 3.
Step 3: Bring down 88, making it the new dividend. Add the old divisor with the same number 3 + 3, which gives us 6 as the beginning of our new divisor.
Step 4: Find a digit, say m, such that 6m x m is ≤ 388. The closest we get is 64 x 4 = 256.
Step 5: Subtract 256 from 388, yielding a remainder of 132.
Step 6: Since the dividend is less than the divisor, we add a decimal point and bring down two zeroes. The new dividend is 13200.
Step 7: Repeat these steps until we get two numbers after the decimal point. The process continues to yield more precise decimal places.
So the square root of √1288 is approximately 35.877.
Square Root of 1288 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 1288 using the approximation method.
Step 1: Now we have to find the closest perfect squares around 1288. The smallest perfect square less than 1288 is 1225, and the largest perfect square greater than 1288 is 1369. √1288 falls somewhere between 35 and 37.
Step 2: Now we need to apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Applying the formula: (1288 - 1225) / (1369 - 1225) = 63 / 144 ≈ 0.4375. Using the formula, we identified the decimal point of our square root. Adding this to the initial value: 35 + 0.4375 ≈ 35.877, so the square root of 1288 is approximately 35.877.
Common Mistakes and How to Avoid Them in the Square Root of 1288
Students often make mistakes while finding square roots, such as forgetting about the negative square root or skipping steps in the long division method. 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 has both positive and negative square roots. However, we typically consider only the positive square root, as it is the required one.
For example, √50 = 7.07, but there is also -7.07, which should not be forgotten.
Mistake 2
Not adding square root symbol in proper places
Incorrect placement of the square root symbol is another mistake that people make. To resolve this, we need to teach that simplifying the numbers inside the square root is important before moving to the next step.
For example, √(12+24) = √36 is correct, not √12 + √24.
Mistake 3
Not finding the correct value of a non-perfect square
The first step that needs to be taught 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 = 7.071067, not 7.
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 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 many steps. Due to this, students might skip a step accidentally, resulting in a wrong answer. This may occur during subtraction or elsewhere in the process.
Square Root of 1288 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √1288?
The area of the square is 1288 square units.
Explanation
The area of the square = side².
The side length is given as √1288.
Area = (√1288)² = 1288.
Therefore, the area of the square box is 1288 square units.
Problem 2
A square-shaped building measuring 1288 square feet is built. If each of the sides is √1288, what will be the square feet of half of the building?
644 square feet
Explanation
We can just divide the given area by 2 since the building is square-shaped.
Dividing 1288 by 2 = 644.
So half of the building measures 644 square feet.
Problem 3
Calculate √1288 x 5.
179.385
Explanation
The first step is to find the square root of 1288, which is approximately 35.877.
The second step is to multiply 35.877 by 5.
So 35.877 x 5 ≈ 179.385.
Problem 4
What will be the square root of (1200 + 88)?
The square root is approximately 35.877
Explanation
To find the square root, we need to find the sum of (1200 + 88), which is 1288, and then find the square root of 1288, which is approximately 35.877.
Therefore, the square root of (1200 + 88) is approximately ±35.877.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √1288 units and the width ‘w’ is 50 units.
The perimeter of the rectangle is approximately 171.754 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√1288 + 50) = 2 × (35.877 + 50) ≈ 2 × 85.877 = 171.754 units.
FAQ on Square Root of 1288
1.What is √1288 in its simplest form?
2.Mention the factors of 1288.
3.Calculate the square of 1288.
4.Is 1288 a prime number?
5.1288 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 1288?
8.How do technology and digital tools in Australia support learning Algebra and Square Root of 1288?
9.Does learning Algebra support future career opportunities for students in Australia?
Important Glossaries for the Square Root of 1288
- Square root: A square root is the inverse of a square. Example: 4^2 = 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.
- Principal square root: A number has both positive and negative square roots; however, it is usually the positive square root that is used in practical applications. This is known as the principal square root.
- Long division method: A method used to find the square root of non-perfect squares by a series of steps involving division and subtraction.
- Prime factorization: Breaking down a number into its basic prime factors, which can help in simplifying radical expressions.
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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.
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