Square Root of 212 - How to Find Square Root of 212? [Solved] (2024)

The square root of 212 is expressed as √212 in the radical form and as (212)^½ or (212)^0.5 in the exponent form. The square root of 212 rounded up to 8 decimal places is 14.56021978. It is the positive solution of the equation x² = 212. We can express the square root of 212 in its lowest radical form as 2 √53.

Square Root of 212: 14.560219778561036
Square Root of 212 in exponential form: (212)^½ or (212)^0.5
Square Root of 212 in radical form: √212 or 2 √53

1.	What is the Square Root of 212?
2.	How to find the Square Root of 212?
3.	Is the Square Root of 212 Irrational?
4.	FAQs

What is the Square Root of 212?

The square root of 212, (or root 212), is the number which when multiplied by itself gives the product as 212. Therefore, the square root of 212 = √212 = 2 √53 = 14.560219778561036.

☛ Check: Square Root Calculator

How to Find Square Root of 212?

Value of √212 by Long Division Method

Explanation:

Forming pairs: 02 and 12
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 12, to the right of the remainder 1. The new dividend is now 112.
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 <= 112. After finding Z, together 2 and Z (4) form a new divisor 24 for the new dividend 112.
Divide 112 by 24 with the quotient as 4, giving the remainder = 112 - 24 × 4 = 112 - 96 = 16.
Now, let's find the decimal places after the quotient 14.
Bring down 00 to the right of this remainder 16. The new dividend is now 1600.
Add the last digit of quotient to divisor i.e. 4 + 24 = 28. To the right of 28, find a digit Z (which is 5) such that 28Z × Z <= 1600. Together they form a new divisor (285) for the new dividend (1600).
Divide 1600 by 285 with the quotient as 5, giving the remainder = 1600 - 285 × 5 = 1600 - 1425 = 175.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 212.

Therefore, the square root of 212 by long division method is 14.5 approximately.

Is Square Root of 212 Irrational?

The actual value of √212 is undetermined. The value of √212 up to 25 decimal places is 14.56021977856103654219460. Hence, the square root of 212 is an irrational number.

☛ Also Check:

Square Root of 45 - √45 = 6.70820
Square Root of 35 - √35 = 5.91608
Square Root of 240 - √240 = 15.49193
Square Root of 80 - √80 = 8.94427
Square Root of 1296 - √1296 = 36
Square Root of 106 - √106 = 10.29563
Square Root of 729 - √729 = 27

Square Root of 212 Solved Examples

Example 1: Solve the equation x² − 212 = 0
Solution:
x² - 212 = 0 i.e. x² = 212
x = ±√212
Since the value of the square root of 212 is 14.560,
⇒ x = +√212 or -√212 = 14.560 or -14.560.
See Also
What is 212 Divided by 9? With Remainder, as Decimal, etc
Example 2: If the surface area of a cube is 1272 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 = 1272 in²
⇒ a = ±√212 in
Since length can't be negative,
⇒ a = √212
We know that the square root of 212 is 14.560.
⇒ a = 14.560 in
Example 3: If the area of a circle is 212π in². Find the radius of the circle.
Solution:
Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 212π in²
⇒ r = ±√212 in
Since radius can't be negative,
⇒ r = √212
The square root of 212 is 14.560.
⇒ r = 14.560 in

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FAQs on the Square Root of 212

What is the Value of the Square Root of 212?

The square root of 212 is 14.56021.

Why is the Square Root of 212 an Irrational Number?

Upon prime factorizing 212 i.e. 2² × 53¹, 53 is in odd power. Therefore, the square root of 212 is irrational.

If the Square Root of 212 is 14.560. Find the Value of the Square Root of 2.12.

Let us represent √2.12 in p/q form i.e. √(212/100) = 2.12/10 = 1.456. Hence, the value of √2.12 = 1.456

What is the Square Root of -212?

The square root of -212 is an imaginary number. It can be written as √-212 = √-1 × √212 = i √212 = 14.56i
where i = √-1 and it is called the imaginary unit.

Is the number 212 a Perfect Square?

The prime factorization of 212 = 2² × 53¹. Here, the prime factor 53 is not in the pair. Therefore, 212 is not a perfect square.

What is the Square of the Square Root of 212?

The square of the square root of 212 is the number 212 itself i.e. (√212)² = (212)^2/2 = 212.