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Square Root of 2100

The square root of 2100 is expressed as √2100 in the radical form and as (2100)^½ or (2100)^0.5 in the exponent form. The square root of 2100 rounded up to 9 decimal places is 45.825756950. It is the positive solution of the equation x² = 2100. We can express the square root of 2100 in its lowest radical form as 10 √21.

Square Root of 2100: 45.8257569495584
Square Root of 2100 in exponential form: (2100)^½ or (2100)^0.5
Square Root of 2100 in radical form: √2100 or 10 √21

Square Root of 2100

1.	What is the Square Root of 2100?
2.	How to find the Square Root of 2100?
3.	Is the Square Root of 2100 Irrational?
4.	FAQs

What is the Square Root of 2100?

The square root of 2100, (or root 2100), is the number which when multiplied by itself gives the product as 2100. Therefore, the square root of 2100 = √2100 = 10 √21 = 45.8257569495584.

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How to Find Square Root of 2100?

Square Root of 2100 by Long Division Method

Value of √2100 by Long Division Method

Explanation:

Forming pairs: 21 and 00
Find a number Y (4) such that whose square is <= 21. Now divide 21 by 4 with quotient as 4.
Bring down the next pair 00, to the right of the remainder 5. The new dividend is now 500.
Add the last digit of the quotient (4) to the divisor (4) i.e. 4 + 4 = 8. To the right of 8, find a digit Z (which is 5) such that 8Z × Z <= 500. After finding Z, together 8 and Z (5) form a new divisor 85 for the new dividend 500.
Divide 500 by 85 with the quotient as 5, giving the remainder = 500 - 85 × 5 = 500 - 425 = 75.
Now, let's find the decimal places after the quotient 45.
Bring down 00 to the right of this remainder 75. The new dividend is now 7500.
Add the last digit of quotient to divisor i.e. 5 + 85 = 90. To the right of 90, find a digit Z (which is 8) such that 90Z × Z <= 7500. Together they form a new divisor (908) for the new dividend (7500).
Divide 7500 by 908 with the quotient as 8, giving the remainder = 7500 - 908 × 8 = 7500 - 7264 = 236.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 2100.

Therefore, the square root of 2100 by long division method is 45.8 approximately.

Is Square Root of 2100 Irrational?

The actual value of √2100 is undetermined. The value of √2100 up to 25 decimal places is 45.82575694955840006588047. Hence, the square root of 2100 is an irrational number.

☛ Also Check:

Square Root of 50 - √50 = 7.07107
Square Root of 75 - √75 = 8.66025
Square Root of 256 - √256 = 16
Square Root of 34 - √34 = 5.83095
Square Root of 37 - √37 = 6.08276
Square Root of 21 - √21 = 4.58258
Square Root of 109 - √109 = 10.44031

Square Root of 2100 Solved Examples

Example 1: Solve the equation x² − 2100 = 0

Solution:

x² - 2100 = 0 i.e. x² = 2100
x = ±√2100
Since the value of the square root of 2100 is 45.826,
⇒ x = +√2100 or -√2100 = 45.826 or -45.826.
Example 2: If the surface area of a cube is 12600 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 = 12600 in²
⇒ a = ±√2100 in
Since length can't be negative,
⇒ a = √2100
We know that the square root of 2100 is 45.826.
⇒ a = 45.826 in
Example 3: If the area of an equilateral triangle is 2100√3 in². 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)a² = 2100√3 in²
⇒ a = ±√8400 in
Since length can't be negative,
⇒ a = √8400 = 2 √2100
We know that the square root of 2100 is 45.826.
⇒ a = 91.652 in

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FAQs on the Square Root of 2100

What is the Value of the Square Root of 2100?

The square root of 2100 is 45.82575.

Why is the Square Root of 2100 an Irrational Number?

Upon prime factorizing 2100 i.e. 2² × 3¹ × 5² × 7¹, 3 is in odd power. Therefore, the square root of 2100 is irrational.

What is the Value of 2 square root 2100?

The square root of 2100 is 45.826. Therefore, 2 √2100 = 2 × 45.826 = 91.652.

Evaluate 9 plus 18 square root 2100

The given expression is 9 + 18 √2100. We know that the square root of 2100 is 45.826. Therefore, 9 + 18 √2100 = 9 + 18 × 45.826 = 9 + 824.864 = 833.864

What is the Square of the Square Root of 2100?

The square of the square root of 2100 is the number 2100 itself i.e. (√2100)² = (2100)^2/2 = 2100.

What is the Square Root of -2100?

The square root of -2100 is an imaginary number. It can be written as √-2100 = √-1 × √2100 = i √2100 = 45.825i
where i = √-1 and it is called the imaginary unit.

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