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Last updated on April 7th, 2025

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Square Root of 30625

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If a number is multiplied by the same number, the result is a square. The inverse of the square is a square root. The square root is used in fields such as vehicle design, finance, etc. Here, we will discuss the square root of 30625.

Square Root of 30625 for Thai Students
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What is the Square Root of 30625?

The square root is the inverse of the square of a number. 30625 is a perfect square. The square root of 30625 can be expressed in both radical and exponential form. In the radical form, it is expressed as √30625, whereas (30625)^(1/2) in the exponential form. √30625 = 175, which is a rational number because it can be expressed in the form of p/q, where p and q are integers and q ≠ 0.

square root of 30625

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Finding the Square Root of 30625

The prime factorization method is used for perfect square numbers. For non-perfect square numbers, the long-division method and approximation method are used. Let's now learn the following methods:

 

  • Prime factorization method
  • Long division method
  • Approximation method
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Square Root of 30625 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 30625 is broken down into its prime factors:

 

Step 1: Finding the prime factors of 30625 Breaking it down, we get 5 x 5 x 5 x 5 x 7 x 7: (5^4) x (7^2)

 

Step 2: Now we found the prime factors of 30625. The second step is to make pairs of those prime factors. Since 30625 is a perfect square, each prime factor can be paired.

 

Therefore, the square root of 30625 is the product of one factor from each pair, which is 5 x 5 x 7 = 175.

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Square Root of 30625 by Long Division Method

The long division method is particularly used for non-perfect square numbers but can also confirm the square root of perfect squares. In this method, we check the closest perfect square number for the given number. Let us now learn how to find the square root using the long division method, step by step.

 

Step 1: To begin with, we need to group the numbers from right to left. In the case of 30625, we group it as 30 625.

 

Step 2: Now, we need to find n whose square is 30 or less. We can say n is ‘5’ because 5 x 5 = 25, which is less than 30. Now the quotient is 5, and after subtracting 30 - 25, the remainder is 5.

 

Step 3: Bring down 625, making the new dividend 5625. Add the old divisor with the quotient, 5 + 5 = 10, which becomes the new divisor.

 

Step 4: Find n such that (10n) x n ≤ 5625. Here, n is 5 because (105) x 5 = 525. Step 5: Subtract 5625 from 525, leaving a remainder of 0.

 

Since the remainder is 0, the quotient 175 is the square root of 30625.

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Square Root of 30625 by Approximation Method

The approximation method is useful for finding the square roots, especially for non-perfect squares. However, for perfect squares like 30625, this method confirms the value.

 

Step 1: Find the closest perfect squares around 30625. The smallest perfect square is 30276 (174^2) and the largest is 30976 (176^2). √30625 falls between 174 and 176.

 

Step 2: Since 30625 is closer to the middle of these two squares, the square root is exactly 175.

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Common Mistakes and How to Avoid Them in the Square Root of 30625

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Square Root of 30625 Examples

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Problem 1

Calculate the side length of a square with an area of 30625 square units.

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Explanation

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Problem 2

A square-shaped garden has an area of 30625 square feet. What is the length of one side of the garden?

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Explanation

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Problem 3

What is √30625 x 2?

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Explanation

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Problem 4

What will be the square root of (30625 + 0)?

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Explanation

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Problem 5

Find the perimeter of a square with a side length of √30625 units.

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Explanation

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FAQ on Square Root of 30625

1.What is √30625 in its simplest form?

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2.Mention the factors of 30625.

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3.Calculate the square of 30625.

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4.Is 30625 a prime number?

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5.30625 is divisible by?

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6.How does learning Algebra help students in Thailand make better decisions in daily life?

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7.How can cultural or local activities in Thailand support learning Algebra topics such as Square Root of 30625?

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8.How do technology and digital tools in Thailand support learning Algebra and Square Root of 30625?

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9.Does learning Algebra support future career opportunities for students in Thailand?

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Important Glossaries for the Square Root of 30625

  • Square root: A square root is the inverse of squaring a number. For example: 15^2 = 225, so the square root of 225 is √225 = 15.

 

  • Perfect square: A number that is the square of an integer. For example, 30625 is a perfect square because 175^2 = 30625.

 

  • Rational number: A number that can be expressed as a fraction p/q, where p and q are integers and q is not zero. For example, 175 is a rational number.

 

  • Prime factorization: Expressing a number as the product of its prime factors. For example, the prime factorization of 30625 is 5^4 x 7^2.

 

  • Long division method: A method used to find the square root of a number by dividing it into manageable parts.
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About BrightChamps in Thailand

At BrightChamps, we understand algebra is more than just symbols—it opens up a world of opportunities! Our mission is to help children across Thailand develop essential math skills, focusing today on the Square Root of 30625 with a special look at square roots—in a lively, enjoyable, and easy-to-follow manner. Whether your child is discovering the speed of a roller coaster at Dream World, tallying local football scores, or managing their allowance to buy the latest gadgets, mastering algebra gives them confidence for everyday life. Our interactive lessons make learning fun and straightforward. Since children in Thailand have varied learning styles, we personalize our approach for each child. From Bangkok’s busy streets to Phuket’s tropical islands, BrightChamps brings math to life, making it relatable and exciting throughout Thailand. Let’s make square roots a joyful part of every child’s math journey!
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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.

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Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.

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