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Last updated on May 26th, 2025

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Square Root of 90000

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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 the field of vehicle design, finance, etc. Here, we will discuss the square root of 90000.

Square Root of 90000 for Singaporean Students
Professor Greenline from BrightChamps

What is the Square Root of 90000?

The square root is the inverse of the square of a number. 90000 is a perfect square. The square root of 90000 is expressed in both radical and exponential forms. In radical form, it is expressed as √90000, whereas (90000)^(1/2) in exponential form. √90000 = 300, 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.

Professor Greenline from BrightChamps

Finding the Square Root of 90000

The prime factorization method is used for perfect square numbers. Since 90000 is a perfect square, we can use the prime factorization method and also verify using the long division method. Let us now learn these methods: 

 

  • Prime factorization method 
  • Long division method
Professor Greenline from BrightChamps

Square Root of 90000 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 90000 is broken down into its prime factors.

 

Step 1: Finding the prime factors of 90000 Breaking it down, we get 2 × 2 × 3 × 3 × 5 × 5 × 5 × 5 = 2^2 × 3^2 × 5^4

 

Step 2: Now we found out the prime factors of 90000. The next step is to make pairs of those prime factors. Since 90000 is a perfect square, all the digits of the number can be grouped in pairs.

 

Therefore, calculating the square root using prime factorization is straightforward: √90000 = √(2^2 × 3^2 × 5^4) = 2 × 3 × 5^2 = 300.

Professor Greenline from BrightChamps

Square Root of 90000 by Long Division Method

The long division method is another way to find the square root of numbers, especially perfect squares. 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. For 90000, we group it as (90) (000).

 

Step 2: Now we need to find a number whose square is less than or equal to the first group, 90. We can choose 9, as 9 × 9 = 81. Now the quotient is 9, and the remainder is 90 - 81 = 9.

 

Step 3: Bring down the next pair of zeros to the remainder, making it 900.

 

Step 4: Double the quotient we obtained, which is 9, to get 18.

 

Step 5: Find a digit x such that 18x × x is less than or equal to 900. We find that x = 5, as 185 × 5 = 925, which is greater than 900, so we choose x = 4, as 184 × 4 = 736.

 

Step 6: Subtract 736 from 900, leaving a remainder of 164.

 

Step 7: Bring down the next pair of zeros to make it 16400.

 

Step 8: Now, double the new quotient formed, 94, to get 188.

 

Step 9: Find a digit x such that 188x × x is less than or equal to 16400. x = 8 works, as 1888 × 8 = 15104.

 

Step 10: Subtract 15104 from 16400, leaving a remainder of 1296.

 

Step 11: Continue this process until you reach a remainder of 0 or get the desired precision.

 

The quotient will be 300, confirming that √90000 = 300.

Professor Greenline from BrightChamps

Square Root of 90000 by Approximation Method

The approximation method involves finding the nearest perfect squares around 90000 and estimating the square root accordingly. However, since 90000 is a perfect square, we already know the exact square root is 300.

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Common Mistakes and How to Avoid Them in the Square Root of 90000

Students do make mistakes while finding the square root, such as forgetting about the negative square root or not properly pairing factors. Let's look at a few common mistakes.

Mistake 1

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Forgetting about the negative square root

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It is important to remember that a number has both positive and negative square roots. However, we usually take only the positive square root for practical purposes.

For example, √90000 = 300, but there is also -300, which should not be forgotten.

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Square Root of 90000 Examples

Ray, the Character from BrightChamps Explaining Math Concepts
Max, the Girl Character from BrightChamps

Problem 1

Can you help Max find the area of a square box if its side length is given as √1600?

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The area of the square is 1600 square units.

Explanation

The area of the square = side^2.

The side length is given as √1600.

Area of the square = side^2

= √1600 × √1600

= 40 × 40

= 1600.

Therefore, the area of the square box is 1600 square units.

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Max, the Girl Character from BrightChamps

Problem 2

A square-shaped building measuring 90000 square feet is built; if each of the sides is √90000, what will be the square feet of half of the building?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

45000 square feet

Explanation

We can divide the given area by 2 as the building is square-shaped.

Dividing 90000 by 2 gives 45000.

So half of the building measures 45000 square feet.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 3

Calculate √90000 × 5.

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

1500

Explanation

First, find the square root of 90000, which is 300.

Then multiply 300 by 5. So 300 × 5 = 1500.

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Max, the Girl Character from BrightChamps

Problem 4

What will be the square root of (8100 + 8100)?

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The square root is 90.

Explanation

Find the sum of (8100 + 8100) = 16200.

The square root of 16200 is not straightforward, but since 8100 is a perfect square (90^2), we can simplify calculations.

√16200 ≈ 127.28.

Therefore, the square root of (8100 + 8100) is approximately 127.28.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √160000 units and the width ‘w’ is 200 units.

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

The perimeter of the rectangle is 1600 units.

Explanation

Perimeter of the rectangle = 2 × (length + width)

Perimeter = 2 × (√160000 + 200)

= 2 × (400 + 200)

= 2 × 600

= 1200 units.

Max from BrightChamps Praising Clear Math Explanations
Ray Thinking Deeply About Math Problems

FAQ on Square Root of 90000

1.What is √90000 in its simplest form?

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2.Mention the factors of 90000.

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3.Calculate the square of 300.

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4.Is 90000 a prime number?

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5.90000 is divisible by?

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

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7.How can cultural or local activities in Singapore support learning Algebra topics such as Square Root of 90000?

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8.How do technology and digital tools in Singapore support learning Algebra and Square Root of 90000?

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

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Professor Greenline from BrightChamps

Important Glossaries for the Square Root of 90000

  • Square root: A square root is the inverse of a square. Example: 4^2 = 16, and the inverse of the square is the square root, that is √16 = 4.
     
  • Rational number: A rational number is a number that can be written in the form of p/q, where p and q are integers and q is not equal to zero.
     
  • Perfect square: A perfect square is a number that is the square of an integer. Example: 90000 is a perfect square as it is 300 × 300.
     
  • Prime factorization: Prime factorization is expressing a number as the product of its prime factors. Example: The prime factorization of 90000 is 2^2 × 3^2 × 5^4.
     
  • Long division method: The long division method is a technique used to find the square root of numbers, especially when it involves decimals or non-perfect squares.
Professor Greenline from BrightChamps

About BrightChamps in Singapore

At BrightChamps, we see algebra as more than just symbols—it opens up a world of opportunities! We’re committed to helping children across Singapore develop essential math skills, focusing today on the Square Root of 90000 with a special focus on understanding square roots—in an engaging, lively, and simple way. Whether your child is figuring out how fast a roller coaster speeds at Universal Studios Singapore, keeping track of football match scores, or managing their allowance for the newest gadgets, mastering algebra boosts their confidence in daily life. Our interactive lessons make learning fun and accessible. Because kids in Singapore learn in various ways, we customize our teaching to fit each child’s style. From bustling city streets to scenic gardens, BrightChamps makes math come alive throughout Singapore. Let’s make square roots an exciting part of every child’s math adventure!
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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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Max, the Girl Character from BrightChamps

Fun Fact

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

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