Square Root of 958
2026-02-28 23:48 Diff
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Last updated on August 5, 2025

If a number is multiplied by itself, the result is a square. The inverse of taking the square is finding the square root. The concept of square roots is used in fields such as engineering, finance, and more. Here, we will discuss the square root of 958.

What is the Square Root of 958?

The square root is the inverse operation of squaring a number. Since 958 is not a perfect square, its square root is expressed in both radical and exponential form. In the radical form, it is expressed as √958, and in the exponential form, it is expressed as (958)(1/2). The square root of 958 is approximately equal to 30.935, which is an irrational number because it cannot be expressed as a ratio of two integers.

Finding the Square Root of 958

The prime factorization method works well for perfect squares, but for non-perfect squares like 958, we use the long division method and approximation method. Let us now explore these methods:

  • Prime factorization method
     
  • Long division method
     
  • Approximation method

Square Root of 958 by Prime Factorization Method

The prime factorization of a number is the product of its prime factors. Let's see how 958 can be broken down into its prime factors:

Step 1: Finding the prime factors of 958. Breaking it down, we get 2 x 479. Since 479 is a prime number, there are no further factors.

Step 2: Now that we have the prime factors of 958, it is clear that they cannot be paired completely, as 958 is not a perfect square.

Therefore, calculating the square root of 958 using prime factorization is not feasible.

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Square Root of 958 by Long Division Method

The long division method is suitable for finding the square root of non-perfect squares. Here is how to find the square root of 958 using this method, step by step:

Step 1: Group the numbers from right to left. For 958, we consider it as 9|58.

Step 2: Find a number whose square is less than or equal to 9. That number is 3, because 3 x 3 = 9. Subtracting gives a remainder of 0.

Step 3: Bring down 58 to make the new dividend 58. Double the previous quotient (3) to get 6, which becomes the beginning of the new divisor.

Step 4: Find a digit (n) such that 6n x n is less than or equal to 58. The suitable n is 0, because 60 x 0 = 0.

Step 5: Subtract 0 from 58, leaving 58.

Step 6: Since the dividend is less than the divisor, add a decimal point and two zeroes, making the new dividend 5800.

Step 7: Now find a digit (n) for the new divisor 600 + n such that (60n + n) x n is less than or equal to 5800. The suitable n is 9, because 609 x 9 = 5481.

Step 8: Subtract 5481 from 5800 to get a remainder of 319.

Step 9: The quotient is approximately 30.9.

Step 10: Continue this process to obtain more precision.

So, the square root of √958 is approximately 30.935.

Square Root of 958 by Approximation Method

The approximation method is another way to find square roots, especially when an exact value is not necessary. Here is how to approximate the square root of 958:

Step 1: Find the closest perfect squares around 958. The closest perfect square less than 958 is 961 (312), and the closest perfect square greater is 900 (302). Therefore, √958 falls between 30 and 31.

Step 2: Use linear interpolation to estimate the decimal part. Formula: (Given number - smaller perfect square) / (larger perfect square - smaller perfect square) Applying the formula: (958 - 900) / (961 - 900) = 58 / 61 ≈ 0.951

Step 3: Add this decimal to the smaller integer: 30 + 0.951 ≈ 30.951 Thus, the square root of 958 is approximately 30.951.

Common Mistakes and How to Avoid Them in the Square Root of 958

Students often make errors in calculating square roots, such as ignoring the negative square root or omitting steps in the long division method. Let’s explore some common mistakes and how to avoid them.

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Problem 1

Can you help Max find the area of a square box if its side length is given as √958?

Okay, lets begin

The area of the square is approximately 917.67 square units.

Explanation

The area of the square = side2.

The side length is given as √958.

Area of the square = (√958)2 = 958 square units.

Therefore, the area of the square box is approximately 917.67 square units.

Well explained 👍

Problem 2

A square-shaped building measuring 958 square feet is built; if each of the sides is √958, what will be the square feet of half of the building?

Okay, lets begin

479 square feet

Explanation

The building is square-shaped, so dividing the area by 2 gives half the building's area.

Dividing 958 by 2 = 479.

So, half of the building measures 479 square feet.

Well explained 👍

Problem 3

Calculate √958 x 5.

Okay, lets begin

Approximately 154.675

Explanation

The first step is to find the square root of 958, which is approximately 30.935.

The second step is to multiply 30.935 by 5.

30.935 x 5 ≈ 154.675

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Problem 4

What will be the square root of (950 + 8)?

Okay, lets begin

The square root is approximately 30.935.

Explanation

To find the square root, first find the sum of 950 + 8. 950 + 8 = 958.

Then, √958 ≈ 30.935.

Therefore, the square root of (950 + 8) is approximately ±30.935.

Well explained 👍

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √958 units and the width ‘w’ is 38 units.

Okay, lets begin

The perimeter is approximately 137.87 units.

Explanation

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

Perimeter = 2 × (√958 + 38) ≈ 2 × (30.935 + 38) ≈ 2 × 68.935 ≈ 137.87 units.

Well explained 👍

FAQ on Square Root of 958

1.What is √958 in its simplest form?

The prime factorization of 958 is 2 x 479, and since 479 is prime, the simplest form of √958 is √(2 x 479).

2.Mention the factors of 958.

Factors of 958 are 1, 2, 479, and 958.

3.Calculate the square of 958.

To find the square of 958, multiply the number by itself: 958 x 958 = 917,764.

4.Is 958 a prime number?

No, 958 is not a prime number, as it has more than two factors.

5.What numbers is 958 divisible by?

958 is divisible by 1, 2, 479, and 958.

Important Glossaries for the Square Root of 958

  • Square root: A square root is the inverse of squaring a number. For example, 9^2 = 81, and the square root of 81 is √81 = 9.
  • Irrational number: An irrational number cannot be expressed as a simple fraction. For example, the square root of 2 is an irrational number.
  • Approximation: A method of finding a value that is close to, but not exactly, a precise value.
  • Long division method: A technique to find the square root of a number by dividing it into smaller parts, making it easier to calculate.
  • Prime factorization: Breaking down a composite number into its prime factors. For example, the prime factorization of 18 is 2 x 3 x 3.

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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.