124 LearnersLast updated on May 26th, 2025
Square Root of 1525
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 1525.
What is the Square Root of 1525?
The square root is the inverse of the square of a number. 1525 is not a perfect square. The square root of 1525 is expressed in both radical and exponential form. In the radical form, it is expressed as √1525, whereas 1525^(1/2) in the exponential form. √1525 ≈ 39.05125, 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 1525
The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers, methods like long division and approximation are used. Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 1525 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 1525 is broken down into its prime factors.
Step 1: Finding the prime factors of 1525 Breaking it down, we get 5 x 5 x 61: 5^2 x 61
Step 2: Now we found out the prime factors of 1525. The second step is to make pairs of those prime factors. Since 1525 is not a perfect square, therefore the digits of the number can’t be grouped in pairs completely.
Therefore, calculating 1525 using prime factorization is challenging.
Square Root of 1525 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 1525, we need to group it as 15 and 25.
Step 2: Now we need to find n whose square is 15. We can say n as ‘3’ because 3 x 3 = 9 is less than 15. Now the quotient is 3 after subtracting 9 from 15, the remainder is 6.
Step 3: Now let us bring down 25, making the new dividend 625. Add the old divisor with the same number: 3 + 3, we get 6, which will be our new divisor.
Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 6n as the new divisor, we need to find the value of n.
Step 5: The next step is finding 6n × n ≤ 625. Let us consider n as 10, now 60 x 10 = 600.
Step 6: Subtract 600 from 625, the difference is 25, and the quotient is 30.
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 2500.
Step 8: Now we need to find the new divisor, which is 390 because 390 x 6 = 2340.
Step 9: Subtracting 2340 from 2500, we get the result 160.
Step 10: Now the quotient is 39.0.
Step 11: Continue doing these steps until we get two numbers after the decimal point. Continue until the remainder is zero or a desired precision is achieved.
So the square root of √1525 is approximately 39.05.
Square Root of 1525 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 1525 using the approximation method.
Step 1: Now we have to find the closest perfect square of √1525.
The smallest perfect square of 1525 is 1444, and the largest perfect square is 1600. √1525 falls somewhere between 38 and 40.
Step 2: Now we need to apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square).
Using the formula (1525 - 1444) / (1600 - 1444) = 0.51. 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 38 + 0.51 = 38.51, so the approximate square root of 1525 is 38.51.
Common Mistakes and How to Avoid Them in the Square Root of 1525
Students do 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 common 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 students make. To resolve this, we need to teach students that simplifying the numbers inside the square root is important and then move on to the second step.
For example, √(12+24) ≠ √12 + √24. 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 students 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, resulting in a wrong answer at the end of the sum. This may either happen in subtracting or elsewhere.
Square Root of 1525 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √1525?
The area of the square is 1525 square units.
Explanation
The area of the square = side^2.
The side length is given as √1525.
Area of the square = side^2 = √1525 x √1525 = 1525.
Therefore, the area of the square box is 1525 square units.
Problem 2
A square-shaped building measuring 1525 square feet is built; if each of the sides is √1525, what will be the square feet of half of the building?
762.5 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 1525 by 2 = we get 762.5.
So half of the building measures 762.5 square feet.
Problem 3
Calculate √1525 x 5.
195.26
Explanation
The first step is to find the square root of 1525, which is approximately 39.05.
The second step is to multiply 39.05 by 5.
So 39.05 x 5 ≈ 195.26.
Problem 4
What will be the square root of (1500 + 25)?
The square root is 39.05.
Explanation
To find the square root, we need to find the sum of (1500 + 25). 1500 + 25 = 1525, and then √1525 ≈ 39.05.
Therefore, the square root of (1500 + 25) is approximately ±39.05.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √1525 units and the width ‘w’ is 50 units.
The perimeter of the rectangle is approximately 178.10 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√1525 + 50) ≈ 2 × (39.05 + 50) = 2 × 89.05 = 178.10 units.
FAQ on Square Root of 1525
1.What is √1525 in its simplest form?
2.Mention the factors of 1525.
3.Calculate the square of 1525.
4.Is 1525 a prime number?
5.1525 is divisible by?
6.How does learning Algebra help students in Vietnam make better decisions in daily life?
7.How can cultural or local activities in Vietnam support learning Algebra topics such as Square Root of 1525?
8.How do technology and digital tools in Vietnam support learning Algebra and Square Root of 1525?
9.Does learning Algebra support future career opportunities for students in Vietnam?
Important Glossaries for the Square Root of 1525
- 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.
- Radical form: A way of expressing a number using a root symbol. For example, the radical form of the square root of 16 is √16.
- Exponential form: A way to express the square root of a number using exponents, such as 16^(1/2).
- Prime factorization: The expression of a number as the product of its prime factors. For example, 1525 = 5^2 x 61.
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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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