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 fields such as architecture, finance, etc. Here, we will discuss the square root of 638.
The square root is the inverse operation of squaring a number. 638 is not a perfect square. The square root of 638 is expressed in both radical and exponential form. In the radical form, it is expressed as √638, whereas in exponential form it is (638)^(1/2). √638 ≈ 25.25866, which is an irrational number because it cannot be expressed as a fraction p/q, where p and q are integers and q ≠ 0.
The prime factorization method is typically used for perfect square numbers. However, for non-perfect squares like 638, methods such as the long-division method and approximation method are preferred. Let us explore these methods:
Prime factorization involves expressing a number as a product of its prime factors. Let's explore this for 638:
Step 1: Find the prime factors of 638. Breaking it down, we have 2 x 11 x 29. The prime factorization is 2^1 x 11^1 x 29^1.
Step 2: Since 638 is not a perfect square, its prime factors cannot be paired evenly.
Therefore, finding the square root of 638 via prime factorization is not straightforward.
The long division method is suitable for non-perfect square numbers. Here's how to find the square root of 638 using this method:
Step 1: Group the digits of 638 from right to left. Here, we have 38 and 6.
Step 2: Find the largest number n whose square is less than or equal to 6. This is 2, as 2 x 2 = 4 ≤ 6. The quotient is 2, and the remainder is 6 - 4 = 2.
Step 3: Bring down the next pair of digits (38) to get 238. Double the divisor (2) to get 4, and form the new divisor 4n.
Step 4: Find n such that 4n x n ≤ 238. If n = 5, 45 x 5 = 225.
Step 5: Subtract 225 from 238 to get 13. The quotient becomes 25.
Step 6: Add a decimal, and bring down two zeros to make the dividend 1300.
Step 7: Double the quotient (25) to get 50. Find n such that 50n x n ≤ 1300. If n = 2, 502 x 2 = 1004.
Step 8: Subtract 1004 from 1300 to get 296. Step 9: Continue this process to get more decimal places.
The approximate square root of 638 is 25.258.
The approximation method is another way to find square roots. Here's how to approximate the square root of 638:
Step 1: Identify the perfect squares closest to 638. These are 625 (25^2) and 676 (26^2). Thus, √638 is between 25 and 26.
Step 2: Use the formula for approximation: (Given number - smaller perfect square) / (larger perfect square - smaller perfect square). (638 - 625) / (676 - 625) = 13 / 51 ≈ 0.2549. Adding this to 25 gives 25.2549.
Thus, √638 ≈ 25.258.
Students often make mistakes while finding square roots, such as overlooking the negative square root or skipping steps in methods like long division. Let's explore some common errors and how to avoid them.
Can you help Max find the area of a square box if its side length is given as √638?
The area of the square is 638 square units.
The area of a square = side^2.
The side length is √638.
Area = side^2 = √638 x √638 = 638.
Therefore, the area of the square box is 638 square units.
A square-shaped garden measures 638 square feet; if each side is √638, what will be the area of half of the garden?
319 square feet
Divide the given area by 2 as the garden is square-shaped.
638 ÷ 2 = 319.
So half of the garden measures 319 square feet.
Calculate √638 x 4.
101.03464
First, find the square root of 638, which is approximately 25.25866.
Then multiply by 4.
25.25866 x 4 = 101.03464.
What will be the square root of (600 + 38)?
The square root is 25.25866.
Find the sum: 600 + 38 = 638.
Then the square root of 638 is approximately 25.25866.
Therefore, the square root of (600 + 38) is ±25.25866.
Find the perimeter of a rectangle if its length 'l' is √638 units and the width 'w' is 40 units.
The perimeter of the rectangle is approximately 130.51732 units.
Perimeter of a rectangle = 2 × (length + width).
Perimeter = 2 × (√638 + 40)
= 2 × (25.25866 + 40)
= 2 × 65.25866
≈ 130.51732 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.