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Square root of 58

The number 58 is a special number with only two factors 2 and 29 (both are prime numbers) other than 1 and 58. The square root of a number is a number whose product with itself results in the given number. We will now calculate the square root of 58 using different methods and a few interesting facts and problems as well.

Square root of 58: √58 = 7.6157
Square of 58: 58² = 3364

1.	What Is the Square Root of 58?
2.	Is Square Root of 58 Rational or Irrational?
3.	How to Find the Square Root of 58?
4.	FAQs on Square Root of 58
5.	Important Notes on Square Root of 58

What is The Square Root of 58?

The square root of 58 is √58 = 7.6157.
The number 58 has only two factors that are prime too. So, it cannot be simplified further using prime factorization.
The number 58 is not a perfect square as its square root is not an integer.

Is Square Root of 58 Rational or Irrational?

The square root of 58 is a non-terminating and non-repeating number. So, the square root of 58 is an irrational number as it cannot be expressed in the form of p/q where q ≠ 0.

How to Find the Square root of 58?

Now we will calculate the square root of 58 using the following methods:

Square Root of 58 Using Approximation Method

First, find two consecutive perfect squares between which the number 58 will lie. The two numbers are 49 (7²) and 64 (8²). Therefore, the whole number part of the square root of 58 will be 7.
Now, for the decimal part, we will use the below-mentioned formula: (Given number – Smaller perfect square) / (Greater perfect square – smaller perfect square) = (58 - 49)/(64 - 49) = 9/15 = 0.60
Hence, the square root of 58 via the approximation method is 7.60.

Square Root of 58 By Long Division

We will now calculate the square root of 58 by the long division method with the help of the below-given steps.

Start Grouping the digits from the right side in pairs of two by putting a bar on top of them. We get one pair in this case (58).
Find a number(n) which when multiplied with itself n × n ≤ 58. So, n will be 7 as 7 × 7 = 49.
Now we get the remainder 9 (as 58 - 49 = 9) and the quotient as 7. Also, we have to add the divisor n with itself to get the new divisor. The new divisor here will be 14.
Add a decimal in the dividend and quotient part simultaneously. Also, add 3 pairs of zero in the dividend part.
Bring down the pair of zero. So, our new dividend is 900. Now find a number(m) such that 14m × m ≤ 900. The number m will be 6 as 146 × 6 = 876 ≤ 900.
Repeat the above step for all the pairs of zero.

Square Root of 58

So, we get the square root of √58 = 7.615 by the long division method.

Explore square roots using illustrations and interactive examples.

Important Notes:

The number 58 is not a perfect square.
The square root of 58 is an irrational number.
The square root of -58 is an imaginary number.

Example 1: Dave wants to find out the square root of -58. Can you help Dave?

Solution:

The square root of negative numbers is an imaginary number. Because the square of any number (positive or negative) will result in a positive number. So, the square of -58 is written as √-58 = ±7.615i (where i = √-1).
Example 2: How much minimum area in square feet should be removed from land with a surface area of 58 square feet, such that it can be converted into a garden of square shape with a length of its side as an integer?

Solution:
To make the land of area 58 square feet into a perfect square we should subtract it with a number (a) such that 58 - a = 49 (closest perfect square). Therefore, a = 58 - 49 = 9 square feet.

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FAQs on Square Roots of 58

What is the negative square root of 58?

The negative square root of 58 will be -7.615.

What is the square root of 58 up to 8 decimal places?

The square root of 58 up to 8 decimal places is 7.61577310.

Can we find the square root of 58 using prime factorization form?

No, we can’t find the square root of 58 using the prime factorization method. Because the number 58 has only two factors that too prime. So, we can’t simplify it further.

Is the square root of 58 is a rational number?

No, the square root of 58 is not a rational number. Because it cannot be represented in the form of p/q where q ≠ 0.

How is the square root of 58 is expressed in exponential and radical form?

The square root of 58 is represented as (58)^1/2 in exponential form.
The square root of 58 is represented as √58 in radical form.

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