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Square Root of 210

The square root of 210 is expressed as √210 in the radical form and as (210)^½ or (210)^0.5 in the exponent form. The square root of 210 rounded up to 10 decimal places is 14.4913767462. It is the positive solution of the equation x² = 210.

Square Root of 210: 14.491376746189438
Square Root of 210 in exponential form: (210)^½ or (210)^0.5
Square Root of 210 in radical form: √210

Square Root of 210

1.	What is the Square Root of 210?
2.	How to find the Square Root of 210?
3.	Is the Square Root of 210 Irrational?
4.	FAQs

What is the Square Root of 210?

The square root of 210, (or root 210), is the number which when multiplied by itself gives the product as 210. Therefore, the square root of 210 = √210 = 14.491376746189438.

☛ Check: Square Root Calculator

How to Find Square Root of 210?

Square Root of 210 by Long Division Method

Value of √210 by Long Division Method

Explanation:

Forming pairs: 02 and 10
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 10, to the right of the remainder 1. The new dividend is now 110.
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 <= 110. After finding Z, together 2 and Z (4) form a new divisor 24 for the new dividend 110.
Divide 110 by 24 with the quotient as 4, giving the remainder = 110 - 24 × 4 = 110 - 96 = 14.
Now, let's find the decimal places after the quotient 14.
Bring down 00 to the right of this remainder 14. The new dividend is now 1400.
Add the last digit of quotient to divisor i.e. 4 + 24 = 28. To the right of 28, find a digit Z (which is 4) such that 28Z × Z <= 1400. Together they form a new divisor (284) for the new dividend (1400).
Divide 1400 by 284 with the quotient as 4, giving the remainder = 1400 - 284 × 4 = 1400 - 1136 = 264.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 210.

Therefore, the square root of 210 by long division method is 14.4 approx.

Is Square Root of 210 Irrational?

The actual value of √210 is undetermined. The value of √210 up to 25 decimal places is 14.49137674618943857371866. Hence, the square root of 210 is an irrational number.

☛ Also Check:

Square Root of 63 - √63 = 7.93725
Square Root of 37 - √37 = 6.08276
Square Root of 361 - √361 = 19
Square Root of 729 - √729 = 27
Square Root of 45 - √45 = 6.70820
Square Root of 120 - √120 = 10.95445
Square Root of 256 - √256 = 16

Square Root of 210 Solved Examples

Example 1: Solve the equation x² − 210 = 0

Solution:

x² - 210 = 0 i.e. x² = 210
x = ±√210
Since the value of the square root of 210 is 14.491,
⇒ x = +√210 or -√210 = 14.491 or -14.491.
Example 2: If the area of a square is 210 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 = 210 in²
⇒ a = ±√210 in
Since length can't be negative,
⇒ a = √210 = 14.491 in
Example 3: If the surface area of a cube is 1260 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 = 1260 in²
⇒ a = ±√210 in
Since length can't be negative,
⇒ a = √210
We know that the square root of 210 is 14.491.
⇒ a = 14.491 in

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FAQs on the Square Root of 210

What is the Value of the Square Root of 210?

The square root of 210 is 14.49137.

Why is the Square Root of 210 an Irrational Number?

Upon prime factorizing 210 i.e. 2¹ × 3¹ × 5¹ × 7¹, 2 is in odd power. Therefore, the square root of 210 is irrational.

What is the Square of the Square Root of 210?

The square of the square root of 210 is the number 210 itself i.e. (√210)² = (210)^2/2 = 210.

What is the Square Root of 210 in Simplest Radical Form?

We need to express 210 as the product of its prime factors i.e. 210 = 2 × 3 × 5 × 7. Therefore, as visible, the radical form of the square root of 210 cannot be simplified further. Therefore, the simplest radical form of the square root of 210 can be written as √210

What is the Value of 2 square root 210?

The square root of 210 is 14.491. Therefore, 2 √210 = 2 × 14.491 = 28.983.

Evaluate 3 plus 4 square root 210

The given expression is 3 + 4 √210. We know that the square root of 210 is 14.491. Therefore, 3 + 4 √210 = 3 + 4 × 14.491 = 3 + 57.966 = 60.966

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