Last updated on May 26th, 2025
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.
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.
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:
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.
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.
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.
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.
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.
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.
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
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.
Calculate √1521 x 5.
195
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.
What will be the square root of (1444 + 77)?
The square root is 40.
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.
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.
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√1521 + 38) = 2 × (39 + 38) = 2 × 77 = 154 units.
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.
: He loves to play the quiz with kids through algebra to make kids love it.