143 LearnersLast updated on May 26th, 2025
Square Root of 1521
If a number is multiplied by itself, the result is a square. The inverse of squaring a number is finding its square root. The square root is used in various fields such as vehicle design, finance, etc. Here, we will discuss the square root of 1521.
What is the Square Root of 1521?
The square root is the inverse operation of squaring a number. 1521 is a perfect square. The square root of 1521 can be expressed in both radical and exponential forms. In radical form, it is expressed as √1521, whereas in exponential form, it is expressed as (1521)^(1/2). √1521 = 39, which is a rational number because it can be expressed as the fraction 39/1.
Finding the Square Root of 1521
The prime factorization method is useful for perfect square numbers. For non-perfect squares, the long division and approximation methods are used. For 1521, we will use the prime factorization method:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 1521 by Prime Factorization Method
The prime factorization of a number involves expressing it as a product of its prime factors. Let us look at how 1521 is broken down into its prime factors:
Step 1: Find the prime factors of 1521. Breaking it down, we get 3 x 3 x 13 x 13: 3^2 x 13^2
Step 2: Now that we have found the prime factors of 1521, we can pair them. Since 1521 is a perfect square, the prime factors can be grouped into pairs. Step 3:
The square root of 1521 is the product of one element from each pair: 3 x 13 = 39.
Square Root of 1521 by Long Division Method
The long division method can also be used for finding the square root of perfect squares. Here is how to do it step by step:
Step 1: Group the digits of 1521 from right to left. We have 15 and 21.
Step 2: Find the largest integer n whose square is less than or equal to 15. This is 3, because 3 x 3 = 9. Subtract 9 from 15 to get the remainder 6.
Step 3: Bring down the next pair of digits, 21, to get 621.
Step 4: Double the quotient obtained so far (which is 3) to get 6. Find a digit n such that 6n x n is less than or equal to 621. Here, n = 9, because 69 x 9 = 621.
Step 5: Subtract 621 from 621 to get a remainder of 0.
Thus, the quotient is 39, and the square root of 1521 is 39.
Square Root of 1521 by Approximation Method
The approximation method is generally used for non-perfect squares, but let's consider it briefly for understanding:
Step 1: Find the closest perfect squares. 1521 is itself a perfect square.
Step 2: Using the approximation method would involve calculating the intermediate values but is unnecessary here because 1521 is exactly 39^2.
Thus, the square root of 1521 is 39.
Common Mistakes and How to Avoid Them in the Square Root of 1521
Students often make mistakes while finding square roots, such as forgetting about negative square roots or skipping steps in the long division method. Let's look at a few common mistakes in detail.
Mistake 1
Forgetting about the negative square root
It is important to remember that a number has both positive and negative square roots. However, we generally consider only the positive square root for practical purposes.
For example, √1521 = 39, but there is also -39.
Mistake 2
Not adding the square root symbol in proper places
Incorrect placement of the square root symbol is a common mistake. It's important to simplify the numbers inside the square root before proceeding.
For example, √(9 + 16) ≠ √9 + √16. The correct expression is √(9 + 16) = √25 = 5.
Mistake 3
Not finding the correct value of a non-perfect square
It's crucial to simplify the numbers inside the square root to avoid mistakes. This is more relevant for non-perfect squares.
For example, √50 ≠ 7; the correct approximation is √50 ≈ 7.071.
Mistake 4
Confusing the square root symbol with the cube root
Students often confuse square roots with cube roots. These are different operations.
For example, √64 = 8, but ∛64 = 4.
Mistake 5
Making mistakes in long division
Finding a square root using the long division method involves multiple steps, making it easy to skip a step accidentally, which results in a wrong answer. Maintaining focus and checking each step is crucial.
Square Root of 1521 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √1521?
The area of the square is 1521 square units.
Explanation
The area of a square is given by side^2.
The side length is given as √1521.
Area of the square = side^2 = √1521 x √1521 = 39 x 39 = 1521.
Therefore, the area of the square box is 1521 square units.
Problem 2
A square-shaped building measuring 1521 square feet is built; if each of the sides is √1521, what will be the square feet of half of the building?
760.5 square feet
Explanation
We can divide the given area by 2 as the building is square-shaped.
Dividing 1521 by 2 gives us 760.5 square feet.
So, half of the building measures 760.5 square feet.
Problem 3
Calculate √1521 x 5.
195
Explanation
The first step is to find the square root of 1521, which is 39.
The second step is to multiply 39 by 5.
So, 39 x 5 = 195.
Problem 4
What will be the square root of (1444 + 77)?
The square root is 40.
Explanation
To find the square root, we need to find the sum of (1444 + 77). 1444 + 77 = 1521, and √1521 = 39.
Therefore, the square root of (1444 + 77) is ±39.
Problem 5
Find the perimeter of the rectangle if its length 'l' is √1521 units and the width 'w' is 38 units.
The perimeter of the rectangle is 154 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√1521 + 38) = 2 × (39 + 38) = 2 × 77 = 154 units.
FAQ on Square Root of 1521
1.What is √1521 in its simplest form?
2.Mention the factors of 1521.
3.Calculate the square of 39.
4.Is 1521 a prime number?
5.1521 is divisible by?
6.How does learning Algebra help students in Saudi Arabia make better decisions in daily life?
7.How can cultural or local activities in Saudi Arabia support learning Algebra topics such as Square Root of 1521?
8.How do technology and digital tools in Saudi Arabia support learning Algebra and Square Root of 1521?
9.Does learning Algebra support future career opportunities for students in Saudi Arabia?
Important Glossaries for the Square Root of 1521
- Square root: A square root is the inverse operation of squaring a number. For example, 6^2 = 36, and the inverse is the square root, √36 = 6.
- Perfect square: A perfect square is a number that is the square of an integer. For example, 1521 is a perfect square because it is 39^2.
- Rational number: A rational number can be expressed as a fraction p/q, where p and q are integers and q ≠ 0.
- Prime factorization: Prime factorization involves expressing a number as a product of its prime factors.
- Integer: An integer is a whole number that can be positive, negative, or zero. For example, -5, 0, 3, and 7 are integers.
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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.
