Square Root of 130
The square root of 130 is expressed as √130 in the radical form and as (130)^{½} or (130)^{0.5} in the exponent form. The square root of 130 rounded up to 5 decimal places is 11.40175. It is the positive solution of the equation x^{2} = 130.
 Square Root of 130: 11.40175425099138
 Square Root of 130 in exponential form: (130)^{½} or (130)^{0.5}
 Square Root of 130 in radical form: √130
1.  What Is the Square Root of 130? 
2.  Is Square Root of 130 Rational or Irrational? 
3.  How to Find the Square Root of 130? 
4.  FAQs on Square Root of 130 
5.  Important Notes on Square Root of 130 
What Is the Square Root of 130?
 The square root of 130 is written as √130 in the radical form.
 The square root of 130 is written as (130)^{1/2} in the exponential form.
 The square root of 130 in the decimal form is 11.4017
Is the Square Root of 130 Rational or Irrational?
The square root of 130 is not a natural number.
A rational number is defined as a number that can be represented in the form of p/q, where q ≠ 0.
The square root of 130 cannot be written in the form of p/q. Therefore, the square root of 130 is an irrational number.
How to Find the Square Root of 130?
We will now calculate the square root of 130 using the belowgiven methods:
Square Root of 130 Using Approximation Method
 First, we will find the two consecutive perfect squares between which 130 lies.
In this case, the perfect squares are 121 (11^{2}) and 144 (12^{2}). So, the whole number part of the square root of 130 is 11.  Now, for the decimal part we will use the below formula:
(Given number – Smaller perfect square) / (Greater perfect square – smaller perfect square)
= (130 – 121)/(144 – 121) = 9/23 = 0.391  Hence, the approx. value of the square root of 130 by the approximation method is 11.391
Square Root of 130 By Long Division
Now we will calculate the square root of 130 by the long division method.
 Start grouping the digits from the unit’s place in pairs of two by placing a bar above them. In the case of 130, we will have two pairs: 30 and 1(pairing from the right).
 Now, find a number(t) whose square is ≤ 1. The value of t will be 1 as 1 × 1 = 1≤ 1.
 We get 1 as the quotient. Now, add the divisor t with itself and get the new divisor which is 2t or 2.
 Drag the next pair of digits. The new dividend is 030. Now find a number (N) such that 2N × N ≤ 30. The value of N is 1.
 Now, place a decimal in the dividend (130) and quotient (11). Also, add 3 pairs of zero in the dividend after the decimal and repeat the above steps for the remaining three pairs of zero.
Thus, we get the value of the square root of √130 = 11.401 by the long division method.
Explore square roots using illustrations and interactive examples:
Important Notes:
 The square root of 130 is an irrational number.
 The number 130 is not a perfect square.
 The square root of 130 is an imaginary number.
Square Root of 130 Solved Examples

Example 1: What is the % error in the value of √130 calculated via the approximation method?
Solution:
The value of √130 by the approximation method = 11.391
The actual value of the square root of 130 = 11.4017
Error in the value of √130 = 11.4017 – 11.391 = 0.0107
% Error = (0.0107/11.4017) × 100 = 0.09% 
Example 2: √130 + √130 is the square root of which number?
Solution:
The value of √130 + √130 = 2√130
We know that 2√130 = √(130 × 2 × 2) = √520
Therefore, √130 + √130 is the square root of 520. 
Example: If the surface area of a sphere is 520π in^{2}. Find the radius of the sphere.
Solution:
Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr^{2} = 520π in^{2}
⇒ r = ±√130 in
Since radius can't be negative,
⇒ r = √130
The square root of 130 is 11.402.
⇒ r = 11.402 in
FAQs on the Square Root of 130
What is the Value of the Square Root of 130?
The square root of 130 is 11.40175.
Why is the Square Root of 130 an Irrational Number?
Upon prime factorizing 130 i.e. 2^{1} × 5^{1} × 13^{1}, 2 is in odd power. Therefore, the square root of 130 is irrational.
What is the Value of 8 square root 130?
The square root of 130 is 11.402. Therefore, 8 √130 = 8 × 11.402 = 91.214.
What is the Square of the Square Root of 130?
The square of the square root of 130 is the number 130 itself i.e. (√130)^{2} = (130)^{2/2} = 130.
Evaluate 8 plus 20 square root 130
The given expression is 8 + 20 √130. We know that the square root of 130 is 11.402. Therefore, 8 + 20 √130 = 8 + 20 × 11.402 = 8 + 228.035 = 236.035
What is the Square Root of 130 in Simplest Radical Form?
We need to express 130 as the product of its prime factors i.e. 130 = 2 × 5 × 13. Therefore, as visible, the radical form of the square root of 130 cannot be simplified further. Therefore, the simplest radical form of the square root of 130 can be written as √130
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