Square Root of 215
The square root of 215 is expressed as √215 in the radical form and as (215)^{½} or (215)^{0.5} in the exponent form. The square root of 215 rounded up to 5 decimal places is 14.66288. It is the positive solution of the equation x^{2} = 215.
 Square Root of 215: 14.66287829861518
 Square Root of 215 in exponential form: (215)^{½} or (215)^{0.5}
 Square Root of 215 in radical form: √215
1.  What is the Square Root of 215? 
2.  How to find the Square Root of 215? 
3.  Is the Square Root of 215 Irrational? 
4.  FAQs 
What is the Square Root of 215?
The square root of 215, (or root 215), is the number which when multiplied by itself gives the product as 215. Therefore, the square root of 215 = √215 = 14.66287829861518.
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How to Find Square Root of 215?
Value of √215 by Long Division Method
Explanation:
 Forming pairs: 02 and 15
 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 15, to the right of the remainder 1. The new dividend is now 115.
 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 4) such that 2Z × Z <= 115. After finding Z, together 2 and Z (4) form a new divisor 24 for the new dividend 115.
 Divide 115 by 24 with the quotient as 4, giving the remainder = 115  24 × 4 = 115  96 = 19.
 Now, let's find the decimal places after the quotient 14.
 Bring down 00 to the right of this remainder 19. The new dividend is now 1900.
 Add the last digit of quotient to divisor i.e. 4 + 24 = 28. To the right of 28, find a digit Z (which is 6) such that 28Z × Z <= 1900. Together they form a new divisor (286) for the new dividend (1900).
 Divide 1900 by 286 with the quotient as 6, giving the remainder = 1900  286 × 6 = 1900  1716 = 184.
 Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 215.
Therefore, the square root of 215 by long division method is 14.6 approximately.
Is Square Root of 215 Irrational?
The actual value of √215 is undetermined. The value of √215 up to 25 decimal places is 14.66287829861518014502249. Hence, the square root of 215 is an irrational number.
☛ Also Check:
 Square Root of 75  √75 = 8.66025
 Square Root of 51  √51 = 7.14143
 Square Root of 28  √28 = 5.29150
 Square Root of 325  √325 = 18.02776
 Square Root of 400  √400 = 20
 Square Root of 192  √192 = 13.85641
 Square Root of 225  √225 = 15
Square Root of 215 Solved Examples

Example 1: Solve the equation x^{2} − 215 = 0
Solution:
x^{2}  215 = 0 i.e. x^{2} = 215
x = ±√215
Since the value of the square root of 215 is 14.663,
⇒ x = +√215 or √215 = 14.663 or 14.663. 
Example 2: If the area of an equilateral triangle is 215√3 in^{2}. Find the length of one of the sides of the triangle.
Solution:
Let 'a' be the length of one of the sides of the equilateral triangle.
⇒ Area of the equilateral triangle = (√3/4)a^{2} = 215√3 in^{2}
⇒ a = ±√860 in
Since length can't be negative,
⇒ a = √860 = 2 √215
We know that the square root of 215 is 14.663.
⇒ a = 29.326 in 
Example 3: If the area of a square is 215 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} = 215 in^{2}
⇒ a = ±√215 in
Since length can't be negative,
⇒ a = √215 = 14.663 in
FAQs on the Square Root of 215
What is the Value of the Square Root of 215?
The square root of 215 is 14.66287.
Why is the Square Root of 215 an Irrational Number?
Upon prime factorizing 215 i.e. 5^{1} × 43^{1}, 5 is in odd power. Therefore, the square root of 215 is irrational.
Evaluate 7 plus 9 square root 215
The given expression is 7 + 9 √215. We know that the square root of 215 is 14.663. Therefore, 7 + 9 √215 = 7 + 9 × 14.663 = 7 + 131.966 = 138.966
Is the number 215 a Perfect Square?
The prime factorization of 215 = 5^{1} × 43^{1}. Here, the prime factor 5 is not in the pair. Therefore, 215 is not a perfect square.
What is the Square of the Square Root of 215?
The square of the square root of 215 is the number 215 itself i.e. (√215)^{2} = (215)^{2/2} = 215.
What is the Square Root of 215?
The square root of 215 is an imaginary number. It can be written as √215 = √1 × √215 = i √215 = 14.662i
where i = √1 and it is called the imaginary unit.