120 LearnersLast updated on May 26th, 2025
Square Root of 4900
If a number is multiplied by itself, the result is a square. The inverse of a square is a square root. The square root is used in various fields including vehicle design and finance. Here, we will discuss the square root of 4900.
What is the Square Root of 4900?
The square root is the inverse of squaring a number. 4900 is a perfect square. The square root of 4900 can be expressed in both radical and exponential forms. In radical form, it is expressed as √4900, whereas in exponential form it is (4900)^(1/2). √4900 = 70, which is a rational number because it can be expressed in the form of p/q, where p and q are integers with q ≠ 0.
Finding the Square Root of 4900
For perfect square numbers like 4900, the prime factorization method is often used. We can also use the long division method and approximation method, though they are more common for non-perfect squares. Let us explore these methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 4900 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Let us break down 4900 into its prime factors:
Step 1: Finding the prime factors of 4900
Breaking it down, we get 2 × 2 × 5 × 5 × 7 × 7: 2^2 × 5^2 × 7^2
Step 2: Now that we have found the prime factors of 4900, we make pairs of those prime factors. Since 4900 is a perfect square, the digits of the number can be grouped in pairs. Therefore, the square root of 4900 using prime factorization is possible. Thus, √4900 = √(2^2 × 5^2 × 7^2) = 2 × 5 × 7 = 70.
Square Root of 4900 by Long Division Method
The long division method can also be used for finding the square root of perfect square numbers. Let us learn how to find the square root using the long division method, step by step:
Step 1: To begin, we need to group the numbers from right to left in pairs. In the case of 4900, we group it as 49 and 00.
Step 2: Now we find a number whose square is less than or equal to 49. The number is 7 because 7 × 7 = 49. The quotient is 7, and the remainder is 0.
Step 3: Now, bring down the next pair of zeros, making it 00.
Step 4: Add the old divisor with the same number, 7 + 7 = 14, which will be our new divisor.
Step 5: Determine a number n such that 14n × n is less than or equal to 00. Here n is 0, because 140 × 0 = 0.
Step 6: Subtracting gives us 0 as the remainder.
Step 7: The quotient is 70, which is the square root of 4900.
Square Root of 4900 by Approximation Method
The approximation method is straightforward for finding square roots. Let us learn how to find the square root of 4900 using this method:
Step 1: Find the closest perfect squares to √4900. The closest perfect squares are 4900 itself (exact) and no need for approximation.
Step 2: √4900 = 70 since it is a perfect square.
Common Mistakes and How to Avoid Them in the Square Root of 4900
Students often make mistakes while finding square roots, such as forgetting about the negative square root or applying incorrect methods. Let's look at a few common mistakes in detail.
Mistake 1
Forgetting about the negative square root
It is important to remember that numbers have both positive and negative square roots. However, we generally consider only the positive square root, as it is usually required.
For example: √4900 = 70, but -70 is also a square root that should not be forgotten.
Mistake 2
Not adding the square root symbol in the proper places
Improper use of the square root symbol is a common mistake. To resolve this, teach students to simplify the numbers inside the square root first.
For example: √(9 + 16) ≠ √9 + √16.
The correct approach is √(9 + 16) = √25 = 5.
Mistake 3
Not finding the correct value of a non-perfect square
For perfect squares like 4900, this isn't an issue, but for non-perfect squares, ensure students simplify inside the square root for approximate values.
For example: √50 ≈ 7.071.
Mistake 4
Confusing the square root symbol with the cube root
Students should be taught the difference between cube roots and square roots to avoid confusion.
For example: √8 and ∛8 are different.
Mistake 5
Making mistakes in long division
Finding a square root using the long division method involves several steps. Students might skip steps accidentally, leading to wrong answers. Careful attention to each step is necessary.
Square root of 4900 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √4900?
The area of the square is 4900 square units.
Explanation
The area of a square is calculated as side^2.
The side length is given as √4900.
Area of the square = (√4900) × (√4900) = 70 × 70 = 4900
Therefore, the area of the square box is 4900 square units.
Problem 2
A square-shaped building measuring 4900 square feet is built; if each of its sides is √4900, what will be the square feet of half of the building?
2450 square feet
Explanation
Since the building is square-shaped, we divide the given area by 2.
Dividing 4900 by 2 gives us 2450.
So, half of the building measures 2450 square feet.
Problem 3
Calculate √4900 × 5.
350
Explanation
The first step is finding the square root of 4900, which is 70.
The second step is multiplying 70 by 5.
So, 70 × 5 = 350.
Problem 4
What will be the square root of (4900 + 100)?
The square root is 71.
Explanation
First, find the sum of (4900 + 100) = 5000.
Then find the square root of 5000.
5000 is not a perfect square, but it is close to 4900.
You can approximate it by noting that √4900 = 70 and √5000 is slightly more than 70, approximately 71.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √4900 units and the width ‘w’ is 38 units.
We find the perimeter of the rectangle as 216 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√4900 + 38) = 2 × (70 + 38) = 2 × 108 = 216 units.
FAQ on Square Root of 4900
1.What is √4900 in its simplest form?
2.Mention the factors of 4900.
3.Calculate the square of 4900.
4.Is 4900 a prime number?
5.4900 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 4900?
8.How do technology and digital tools in Saudi Arabia support learning Algebra and Square Root of 4900?
9.Does learning Algebra support future career opportunities for students in Saudi Arabia?
Important Glossaries for the Square Root of 4900
- Square Root: A square root is the value that, when multiplied by itself, gives the original number. Example: 70 × 70 = 4900, so √4900 = 70.
- Perfect Square: A number that is the square of an integer. 4900 is a perfect square because it equals 70^2.
- Rational Number: A number that can be expressed as the quotient or fraction p/q of two integers, where q is not zero. 70 is a rational number.
- Factorization: The process of breaking down a number into its prime components. For example, the prime factorization of 4900 is 2^2 × 5^2 × 7^2.
- Perimeter: The total distance around a two-dimensional shape. For example, the perimeter of a rectangle is calculated as 2 × (length + width).
Explore More algebra
About BrightChamps in Saudi Arabia
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.
