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Square Root of 231
The square root of 231 is expressed as √231 in the radical form and as (231)½ or (231)0.5 in the exponent form. The square root of 231 rounded up to 8 decimal places is 15.19868415. It is the positive solution of the equation x2 = 231.
- Square Root of 231: 15.198684153570664
- Square Root of 231 in exponential form: (231)½ or (231)0.5
- Square Root of 231 in radical form: √231
1. | What is the Square Root of 231? |
2. | How to find the Square Root of 231? |
3. | Is the Square Root of 231 Irrational? |
4. | FAQs |
What is the Square Root of 231?
The square root of 231, (or root 231), is the number which when multiplied by itself gives the product as 231. Therefore, the square root of 231 = √231 = 15.198684153570664.
☛ Check: Square Root Calculator
How to Find Square Root of 231?
Value of √231 by Long Division Method
Explanation:
- Forming pairs: 02 and 31
- Find a number Y (1) such that whose square is <= 2. Now divide 02 by 1 with quotient as 1.
- Bring down the next pair 31, to the right of the remainder 1. The new dividend is now 131.
- 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 5) such that 2Z × Z <= 131. After finding Z, together 2 and Z (5) form a new divisor 25 for the new dividend 131.
- Divide 131 by 25 with the quotient as 5, giving the remainder = 131 - 25 × 5 = 131 - 125 = 6.
- Now, let's find the decimal places after the quotient 15.
- Bring down 00 to the right of this remainder 6. The new dividend is now 600.
- Add the last digit of quotient to divisor i.e. 5 + 25 = 30. To the right of 30, find a digit Z (which is 1) such that 30Z × Z <= 600. Together they form a new divisor (301) for the new dividend (600).
- Divide 600 by 301 with the quotient as 1, giving the remainder = 600 - 301 × 1 = 600 - 301 = 299.
- Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 231.
Therefore, the square root of 231 by long division method is 15.1 approx.
Is Square Root of 231 Irrational?
The actual value of √231 is undetermined. The value of √231 up to 25 decimal places is 15.19868415357066363166874. Hence, the square root of 231 is an irrational number.
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- Square Root of 29 - √29 = 5.38516
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- Square Root of 325 - √325 = 18.02776
- Square Root of 841 - √841 = 29
- Square Root of 125 - √125 = 11.18034
- Square Root of 39 - √39 = 6.24500
- Square Root of 196 - √196 = 14
Square Root of 231 Solved Examples
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Example 1: Solve the equation x2 − 231 = 0
Solution:
x2 - 231 = 0 i.e. x2 = 231
x = ±√231
Since the value of the square root of 231 is 15.199,
⇒ x = +√231 or -√231 = 15.199 or -15.199. -
Example 2: If the surface area of a cube is 1386 in2. Find the length of the side of the cube.
Solution:
Let 'a' be the length of the side of the cube.
⇒ Area of the cube = 6a2 = 1386 in2
⇒ a = ±√231 in
Since length can't be negative,
⇒ a = √231
We know that the square root of 231 is 15.199.
⇒ a = 15.199 in -
Example 3: If the surface area of a sphere is 924π in2. Find the radius of the sphere.
Solution:
Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr2 = 924π in2
⇒ r = ±√231 in
Since radius can't be negative,
⇒ r = √231
The square root of 231 is 15.199.
⇒ r = 15.199 in
FAQs on the Square Root of 231
What is the Value of the Square Root of 231?
The square root of 231 is 15.19868.
Why is the Square Root of 231 an Irrational Number?
Upon prime factorizing 231 i.e. 31 × 71 × 111, 3 is in odd power. Therefore, the square root of 231 is irrational.
What is the Value of 16 square root 231?
The square root of 231 is 15.199. Therefore, 16 √231 = 16 × 15.199 = 243.179.
What is the Square Root of -231?
The square root of -231 is an imaginary number. It can be written as √-231 = √-1 × √231 = i √231 = 15.198i
where i = √-1 and it is called the imaginary unit.
If the Square Root of 231 is 15.199. Find the Value of the Square Root of 2.31.
Let us represent √2.31 in p/q form i.e. √(231/100) = 2.31/10 = 1.520. Hence, the value of √2.31 = 1.520
Evaluate 7 plus 18 square root 231
The given expression is 7 + 18 √231. We know that the square root of 231 is 15.199. Therefore, 7 + 18 √231 = 7 + 18 × 15.199 = 7 + 273.576 = 280.576
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