Square Root of 9.8
2026-02-28 13:16 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-9.8

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Last updated on August 5, 2025

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 various fields like physics, engineering, and finance. Here, we will discuss the square root of 9.8.

What is the Square Root of 9.8?

The square root is the inverse operation of squaring a number. 9.8 is not a perfect square. The square root of 9.8 is expressed in both radical and exponential form. In the radical form, it is expressed as √9.8, whereas in the exponential form it is (9.8)^(1/2). √9.8 ≈ 3.1305, which is an irrational number because it cannot be expressed in the form of p/q, where p and q are integers and q ≠ 0.

Finding the Square Root of 9.8

The prime factorization method is used for perfect square numbers. However, for non-perfect squares like 9.8, approximation methods such as the long-division method are used. Let us now learn the following methods:

  • Long division method
  • Approximation method

Square Root of 9.8 by Long Division Method

The long division method is particularly used for non-perfect square numbers. Let us learn how to find the square root using the long division method, step by step:

Step 1: Start by pairing the digits starting from the decimal point. For 9.8, treat it as 98 under the long division method.

Step 2: Find a number whose square is less than or equal to 9. The closest is 3, since 3 x 3 = 9.

Step 3: Subtract 9 from 9 to get 0, and bring down 80.

Step 4: Double the quotient and bring it down as 6_, looking for a digit that fits.

Step 5: Find a digit 'n' such that (60+n) x n ≤ 80. The suitable n is 1, as 61 x 1 = 61.

Step 6: Subtract 61 from 80 to get 19, then bring down two zeros to get 1900.

Step 7: Repeat the process, finding the next digit and quotient to approximate the square root further.

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Square Root of 9.8 by Approximation Method

Approximation method is another way to find square roots and is useful for quick estimates. Let's find the square root of 9.8 using this method:

Step 1: Identify two perfect squares between which 9.8 falls. It lies between 9 (3^2) and 16 (4^2).

Step 2: Use linear approximation to find the decimal: (9.8 - 9) / (16 - 9) = 0.8 / 7 ≈ 0.1143

Step 3: Add this to the lower bound square root: 3 + 0.1143 ≈ 3.1143.

Thus, the square root of 9.8 ≈ 3.1143.

Common Mistakes and How to Avoid Them in Finding the Square Root of 9.8

Students make common mistakes when calculating square roots, like forgetting about negative roots or mishandling decimals. Here are some common pitfalls:

Problem 1

Can you help Max find the area of a square box if its side length is given as √9.8?

Okay, lets begin

The area of the square is approximately 9.8 square units.

Explanation

The area of a square is given by side^2.

The side length is √9.8.

Therefore, Area = (√9.8)^2 = 9.8.

Well explained 👍

Problem 2

A square-shaped garden measures 9.8 square meters. What is the length of one side?

Okay, lets begin

The length of one side is approximately 3.1305 meters.

Explanation

The length of the side of the square is the square root of the area.

Therefore, side = √9.8 ≈ 3.1305 meters.

Well explained 👍

Problem 3

Calculate √9.8 x 5.

Okay, lets begin

Approximately 15.6525

Explanation

First, find the square root of 9.8, which is approximately 3.1305.

Then multiply by 5: 3.1305 x 5 ≈ 15.6525.

Well explained 👍

Problem 4

What will be the square root of (9.8 + 6)?

Okay, lets begin

The square root is approximately 4.

Explanation

First, calculate the sum: 9.8 + 6 = 15.8.

Then, the square root of 15.8 is approximately 3.976.

Well explained 👍

Problem 5

Find the perimeter of a rectangle if its length ‘l’ is √9.8 units and the width ‘w’ is 5 units.

Okay, lets begin

The perimeter of the rectangle is approximately 16.261 units.

Explanation

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

Perimeter = 2 × (√9.8 + 5) = 2 × (3.1305 + 5) ≈ 2 × 8.1305 = 16.261 units.

Well explained 👍

FAQ on Square Root of 9.8

1.What is √9.8 in its simplest form?

The square root of 9.8 cannot be simplified further into a neat fraction or whole number. It is approximately 3.1305.

2.Can 9.8 be a perfect square?

No, 9.8 is not a perfect square because it does not result from squaring an integer.

3.Calculate the square of 9.8.

The square of 9.8 is 9.8 × 9.8 = 96.04.

4.Is 9.8 a rational number?

Yes, 9.8 is a rational number because it can be expressed as a fraction: 98/10.

5.Is √9.8 a rational number?

No, √9.8 is an irrational number because it cannot be expressed as an exact fraction of two integers.

Important Glossaries for the Square Root of 9.8

  • Square root: The square root of a number is a value that, when multiplied by itself, gives the original number. Example: 3^2=9, so √9=3.
     
  • Irrational number: A number that cannot be expressed as a fraction of two integers. For example, √9.8 is irrational.
     
  • Approximation: The process of finding a value that is close enough to the right answer, usually within a specified range.
     
  • Perfect square: A number that is the square of an integer. For example, 9 is a perfect square since it is 3^2.
     
  • Long division method: A technique used to find the square root of numbers, especially non-perfect squares, using a step-by-step division process.

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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.

Fun Fact

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