Square Root of 143
The square root of 143 is expressed as √143 in the radical form and as (143)^{½} or (143)^{0.5} in the exponent form. The square root of 143 rounded up to 5 decimal places is 11.95826. It is the positive solution of the equation x^{2} = 143.
 Square Root of 143: 11.958260743101398
 Square Root of 143 in exponential form: (143)^{½} or (143)^{0.5}
 Square Root of 143 in radical form: √143
1.  What is the Square Root of 143? 
2.  How to find the Square Root of 143? 
3.  Is the Square Root of 143 Irrational? 
4.  FAQs 
What is the Square Root of 143?
The square root of 143, (or root 143), is the number which when multiplied by itself gives the product as 143. Therefore, the square root of 143 = √143 = 11.958260743101398.
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How to Find Square Root of 143?
Value of √143 by Long Division Method
Explanation:
 Forming pairs: 01 and 43
 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 43, to the right of the remainder 0. The new dividend is now 43.
 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 <= 43. After finding Z, together 2 and Z (1) form a new divisor 21 for the new dividend 43.
 Divide 43 by 21 with the quotient as 1, giving the remainder = 43  21 × 1 = 43  21 = 22.
 Now, let's find the decimal places after the quotient 11.
 Bring down 00 to the right of this remainder 22. The new dividend is now 2200.
 Add the last digit of quotient to divisor i.e. 1 + 21 = 22. To the right of 22, find a digit Z (which is 9) such that 22Z × Z <= 2200. Together they form a new divisor (229) for the new dividend (2200).
 Divide 2200 by 229 with the quotient as 9, giving the remainder = 2200  229 × 9 = 2200  2061 = 139.
 Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 143.
Therefore, the square root of 143 by long division method is 11.9 approx.
Is Square Root of 143 Irrational?
The actual value of √143 is undetermined. The value of √143 up to 25 decimal places is 11.95826074310139802112984. Hence, the square root of 143 is an irrational number.
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Square Root of 143 Solved Examples

Example 1: Solve the equation x^{2} − 143 = 0
Solution:
x^{2}  143 = 0 i.e. x^{2} = 143
x = ±√143
Since the value of the square root of 143 is 11.958,
⇒ x = +√143 or √143 = 11.958 or 11.958. 
Example 2: If the surface area of a cube is 858 in^{2}. 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 = 6a^{2} = 858 in^{2}
⇒ a = ±√143 in
Since length can't be negative,
⇒ a = √143
We know that the square root of 143 is 11.958.
⇒ a = 11.958 in 
Example 3: If the area of a square is 143 in^{2}. 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 = a^{2} = 143 in^{2}
⇒ a = ±√143 in
Since length can't be negative,
⇒ a = √143 = 11.958 in
FAQs on the Square Root of 143
What is the Value of the Square Root of 143?
The square root of 143 is 11.95826.
Why is the Square Root of 143 an Irrational Number?
Upon prime factorizing 143 i.e. 11^{1} × 13^{1}, 11 is in odd power. Therefore, the square root of 143 is irrational.
What is the Square of the Square Root of 143?
The square of the square root of 143 is the number 143 itself i.e. (√143)^{2} = (143)^{2/2} = 143.
What is the Value of 19 square root 143?
The square root of 143 is 11.958. Therefore, 19 √143 = 19 × 11.958 = 227.207.
Evaluate 18 plus 12 square root 143
The given expression is 18 + 12 √143. We know that the square root of 143 is 11.958. Therefore, 18 + 12 √143 = 18 + 12 × 11.958 = 18 + 143.499 = 161.499
Is the number 143 a Perfect Square?
The prime factorization of 143 = 11^{1} × 13^{1}. Here, the prime factor 11 is not in the pair. Therefore, 143 is not a perfect square.