source : cuemath.com

## Square Root of 58 – How to Find the 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

## 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.

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.

## 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.

Is the square root of 58 a rational number – Brainly.com – The square root of 58 is a rational number if 58 is a perfect square.Square Root of 58 Simplified. Square Root of 58 Simplified to simplify the square root of 58 in radical form. Radical 58 simplified gives step by step instructions on how to simplify the square root 58 in simplest radical form. Please enter a number greater than 1.What is -(square root) of 58. Answers: 3 Get. Other questions on the subject: Mathematics. Mathematics, 21.06.2019 20:30, mariahcid904. Find the solution(s) to the system of equations. select all that apply y=x^2-1 y=2x-2. Answers: 2. continue. Mathematics, 22.06.2019 00

Square Root of 58 Simplified – Radical 58 Simplified – The square root of 58 has to be between 7 and 8 because 7^2 is 49 and 8^2 is 64. The answer is 8The largest perfect square factor of 58 = 1 √ 58 = 7.61577 The solution above and all other square root solutions were provided by the Square Root Application .Algebra. Simplify square root of 58. √58 58. The result can be shown in multiple forms. Exact Form:

What is -(square root) of 58 – The square root of 58 is 7.6157731058639.Sqrt 58. Sqrt(58). Find the square root of 58 or any other real number, positive or negative. Here are the answers to questions like: Sqrt 58 or what is the square root of 58? Use the square root calculator below to find the square root of any real number, positive or negative. See also on this page a square root chart 1 to 100.Square Root Of 58? About Number 5. Integers with a last digit as a zero or a five in the decimal system are divisible by five. Five is a prime number. All odd multiples of five border again with the five (all even with zero). The fifth number of the Fibonacci sequence is a five. Five is also the smallest prime number that is the sum of all