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 x² = 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

• 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

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.

We will now calculate the square root of 130 using the below-given 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 (11²) and 144 (12²). 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:

• Square root of 10
• Square root of 5
• Square root of 20
• Square root of 30
• Square root of 13

• 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.