Square Root of 131
The square root of 131 is expressed as √131 in the radical form and as (131)½ or (131)0.5 in the exponent form. The square root of 131 rounded up to 5 decimal places is 11.44552. It is the positive solution of the equation x2 = 131.
- Square Root of 131: 11.445523142259598
- Square Root of 131 in exponential form: (131)½ or (131)0.5
- Square Root of 131 in radical form: √131
1. | What is the Square Root of 131? |
2. | How to find the Square Root of 131? |
3. | Is the Square Root of 131 Irrational? |
4. | FAQs |
What is the Square Root of 131?
The square root of 131, (or root 131), is the number which when multiplied by itself gives the product as 131. Therefore, the square root of 131 = √131 = 11.445523142259598.
☛ Check: Square Root Calculator
How to Find Square Root of 131?
Value of √131 by Long Division Method
Explanation:
- Forming pairs: 01 and 31
- Find a number Y (1) such that whose square is <= 1. Now divide 01 by 1 with quotient as 1.
- Bring down the next pair 31, to the right of the remainder 0. The new dividend is now 31.
- Add the last digit of the quotient (1) to the divisor (1) i.e. 1 + 1 = 2. To the right of 2, find a digit Z (which is 1) such that 2Z × Z <= 31. After finding Z, together 2 and Z (1) form a new divisor 21 for the new dividend 31.
- Divide 31 by 21 with the quotient as 1, giving the remainder = 31 - 21 × 1 = 31 - 21 = 10.
- Now, let's find the decimal places after the quotient 11.
- Bring down 00 to the right of this remainder 10. The new dividend is now 1000.
- Add the last digit of quotient to divisor i.e. 1 + 21 = 22. To the right of 22, find a digit Z (which is 4) such that 22Z × Z <= 1000. Together they form a new divisor (224) for the new dividend (1000).
- Divide 1000 by 224 with the quotient as 4, giving the remainder = 1000 - 224 × 4 = 1000 - 896 = 104.
- Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 131.
Therefore, the square root of 131 by long division method is 11.4 approximately.
Is Square Root of 131 Irrational?
The actual value of √131 is undetermined. The value of √131 up to 25 decimal places is 11.44552314225959703904343. Hence, the square root of 131 is an irrational number.
☛ Also Check:
- Square Root of 21 - √21 = 4.58258
- Square Root of 89 - √89 = 9.43398
- Square Root of 80 - √80 = 8.94427
- Square Root of 92 - √92 = 9.59166
- Square Root of 2 - √2 = 1.41421
- Square Root of 85 - √85 = 9.21954
- Square Root of 75 - √75 = 8.66025
Square Root of 131 Solved Examples
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Example 1: Solve the equation x2 − 131 = 0
Solution:
x2 - 131 = 0 i.e. x2 = 131
x = ±√131
Since the value of the square root of 131 is 11.446,
⇒ x = +√131 or -√131 = 11.446 or -11.446. -
Example 2: If the area of a square is 131 in2. Find the length of the side of the square.
Solution:
Let 'a' be the length of the side of the square.
⇒ Area of the square = a2 = 131 in2
⇒ a = ±√131 in
Since length can't be negative,
⇒ a = √131 = 11.446 in -
Example 3: If the surface area of a sphere is 524π in2. Find the radius of the sphere.
Solution:
Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr2 = 524π in2
⇒ r = ±√131 in
Since radius can't be negative,
⇒ r = √131
The square root of 131 is 11.446.
⇒ r = 11.446 in
FAQs on the Square Root of 131
What is the Value of the Square Root of 131?
The square root of 131 is 11.44552.
Why is the Square Root of 131 an Irrational Number?
The number 131 is prime. This implies that the number 131 is pairless and is not in the power of 2. Therefore, the square root of 131 is irrational.
What is the Square Root of -131?
The square root of -131 is an imaginary number. It can be written as √-131 = √-1 × √131 = i √131 = 11.445i
where i = √-1 and it is called the imaginary unit.
Is the number 131 a Perfect Square?
The number 131 is prime. This implies that the square root of 131 cannot be expressed as a product of two equal integers. Therefore, the number 131 is not a perfect square.
What is the Square of the Square Root of 131?
The square of the square root of 131 is the number 131 itself i.e. (√131)2 = (131)2/2 = 131.
What is the Square Root of 131 in Simplest Radical Form?
The number 131 is a prime number. This implies that the number 131 is pairless and is not in the power of 2. Therefore, the radical form of square root of 131 cannot be simplified further.
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