Last updated on May 26th, 2025
If a number is multiplied by itself, the result is a square. The inverse of squaring is finding a square root. The square root is used in fields like vehicle design, finance, etc. Here, we will discuss the square root of 10100.
The square root is the inverse of squaring a number. 10100 is not a perfect square. The square root of 10100 can be expressed in both radical and exponential forms. In radical form, it is expressed as √10100, whereas in exponential form it is (10100)^(1/2). √10100 ≈ 100.49875, 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 squares. However, for non-perfect squares like 10100, the long-division method and approximation methods are more suitable. Let us now explore these methods:
Prime factorization involves expressing a number as a product of prime factors. Let's see how 10100 is broken down:
Step 1: Finding the prime factors of 10100
Breaking it down, we get 2 x 2 x 5 x 5 x 101: 2^2 x 5^2 x 101
Step 2: Since 10100 is not a perfect square, the digits cannot be grouped into pairs completely. Therefore, calculating √10100 using prime factorization is not straightforward.
The long division method is useful for non-perfect squares. Here's how to find the square root using this method, step by step:
Step 1: Group the digits of 10100 from right to left as 00, 10, and 1.
Step 2: Find n whose square is less than or equal to 1. Here, n is 1 because 1 x 1 = 1. The quotient is 1, and after subtracting, the remainder is 0.
Step 3: Bring down 10, making the new dividend 10. Add the old divisor with itself to get 2, which is the new divisor.
Step 4: Find n such that 2n x n ≤ 10. Here, n is 4, since 2 x 4 x 4 = 8.
Step 5: Subtract 8 from 10 to get 2, and the quotient becomes 14.
Step 6: Bring down the next pair, 00, to make the dividend 200.
Step 7: Find n such that 28n x n ≤ 200. Here, n is 7, since 287 x 7 = 2009, but we should adjust to get 196 as 28 x 7 x 7 = 196.
Step 8: Subtract 196 from 200 to get 4, and the quotient becomes 100.
Step 9: Since the dividend is less than the divisor, add a decimal point and bring down more zeros. Continue this process to get a more precise result.
The square root of 10100 is approximately 100.49875.
The approximation method is a simple way to estimate square roots. Let's find the square root of 10100 using approximation:
Step 1: Identify the closest perfect squares around 10100. The closest are 10000 (100^2) and 10201 (101^2). √10100 lies between 100 and 101.
Step 2: Apply the formula: (Given number - smaller perfect square) / (Larger perfect square - smaller perfect square) (10100 - 10000) ÷ (10201 - 10000) = 100 / 201 ≈ 0.497512
Step 3: Add this decimal to the smaller perfect square's root: 100 + 0.497512 ≈ 100.49875 Therefore, the square root of 10100 is approximately 100.49875.
Students often make mistakes when finding square roots, such as ignoring the negative square root, skipping steps in the long division method, etc. Let's explore some common mistakes in detail.
Can you help Max find the area of a square box if its side length is given as √10100?
The area of the square is approximately 10100 square units.
The area of the square = side^2.
The side length is given as √10100.
Area of the square = side^2 = √10100 x √10100 = 10100.
Therefore, the area of the square box is approximately 10100 square units.
A square-shaped building measuring 10100 square feet is built; if each of the sides is √10100, what will be the square feet of half of the building?
5050 square feet
For a square-shaped building, dividing the given area by 2 gives the area of half the building.
Dividing 10100 by 2 = 5050
So half of the building measures 5050 square feet.
Calculate √10100 x 5.
502.49375
First, find the square root of 10100, which is approximately 100.49875.
Then multiply by 5: 100.49875 x 5 ≈ 502.49375
What will be the square root of (10000 + 100)?
The square root is approximately 100.49875.
To find the square root, sum (10000 + 100), which equals 10100.
The square root of 10100 is approximately 100.49875.
Find the perimeter of a rectangle if its length ‘l’ is √10100 units and the width ‘w’ is 100 units.
The perimeter of the rectangle is approximately 400.99875 units.
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√10100 + 100) Perimeter ≈ 2 × (100.49875 + 100) ≈ 2 × 200.49875 ≈ 400.99875 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.
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