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Square Root of 1800

The square root of 1800 is expressed as √1800 in the radical form and as (1800)^½ or (1800)^0.5 in the exponent form. The square root of 1800 rounded up to 10 decimal places is 42.4264068712. It is the positive solution of the equation x² = 1800. We can express the square root of 1800 in its lowest radical form as 30 √2.

Square Root of 1800: 42.42640687119285
Square Root of 1800 in exponential form: (1800)^½ or (1800)^0.5
Square Root of 1800 in radical form: √1800 or 30 √2

Square Root of 1800

1.	What is the Square Root of 1800?
2.	How to find the Square Root of 1800?
3.	Is the Square Root of 1800 Irrational?
4.	FAQs

What is the Square Root of 1800?

The square root of 1800, (or root 1800), is the number which when multiplied by itself gives the product as 1800. Therefore, the square root of 1800 = √1800 = 30 √2 = 42.42640687119285.

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How to Find Square Root of 1800?

Square Root of 1800 by Long Division Method

Value of √1800 by Long Division Method

Explanation:

Forming pairs: 18 and 00
Find a number Y (4) such that whose square is <= 18. Now divide 18 by 4 with quotient as 4.
Bring down the next pair 00, to the right of the remainder 2. The new dividend is now 200.
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 2) such that 8Z × Z <= 200. After finding Z, together 8 and Z (2) form a new divisor 82 for the new dividend 200.
Divide 200 by 82 with the quotient as 2, giving the remainder = 200 - 82 × 2 = 200 - 164 = 36.
Now, let's find the decimal places after the quotient 42.
Bring down 00 to the right of this remainder 36. The new dividend is now 3600.
Add the last digit of quotient to divisor i.e. 2 + 82 = 84. To the right of 84, find a digit Z (which is 4) such that 84Z × Z <= 3600. Together they form a new divisor (844) for the new dividend (3600).
Divide 3600 by 844 with the quotient as 4, giving the remainder = 3600 - 844 × 4 = 3600 - 3376 = 224.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 1800.

Therefore, the square root of 1800 by long division method is 42.4 approximately.

Is Square Root of 1800 Irrational?

The actual value of √1800 is undetermined. The value of √1800 up to 25 decimal places is 42.42640687119285146405066. Hence, the square root of 1800 is an irrational number.

☛ Also Check:

Square Root of 90 - √90 = 9.48683
Square Root of 76 - √76 = 8.71780
Square Root of 200 - √200 = 14.14214
Square Root of 85 - √85 = 9.21954
Square Root of 40 - √40 = 6.32456
Square Root of 116 - √116 = 10.77033
Square Root of 51 - √51 = 7.14143

Square Root of 1800 Solved Examples

Example 1: Solve the equation x² − 1800 = 0

Solution:

x² - 1800 = 0 i.e. x² = 1800
x = ±√1800
Since the value of the square root of 1800 is 42.426,
⇒ x = +√1800 or -√1800 = 42.426 or -42.426.
Example 2: If the surface area of a sphere is 7200π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 7200π in²
⇒ r = ±√1800 in
Since radius can't be negative,
⇒ r = √1800
The square root of 1800 is 42.426.
⇒ r = 42.426 in
Example 3: If the area of an equilateral triangle is 1800√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 = 1800√3 in²
⇒ a = ±√7200 in
Since length can't be negative,
⇒ a = √7200 = 2 √1800
We know that the square root of 1800 is 42.426.
⇒ a = 84.853 in

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FAQs on the Square Root of 1800

What is the Value of the Square Root of 1800?

The square root of 1800 is 42.4264.

Why is the Square Root of 1800 an Irrational Number?

Upon prime factorizing 1800 i.e. 2³ × 3² × 5², 2 is in odd power. Therefore, the square root of 1800 is irrational.

What is the Value of 8 square root 1800?

The square root of 1800 is 42.426. Therefore, 8 √1800 = 8 × 42.426 = 339.411.

Evaluate 18 plus 16 square root 1800

The given expression is 18 + 16 √1800. We know that the square root of 1800 is 42.426. Therefore, 18 + 16 √1800 = 18 + 16 × 42.426 = 18 + 678.823 = 696.823

What is the Square Root of 1800 in Simplest Radical Form?

We need to express 1800 as the product of its prime factors i.e. 1800 = 2 × 2 × 2 × 3 × 3 × 5 × 5. Therefore, √1800 = √2 × 2 × 2 × 3 × 3 × 5 × 5 = 30 √2. Thus, the square root of 1800 in the lowest radical form is 30 √2.

What is the Square Root of -1800?

The square root of -1800 is an imaginary number. It can be written as √-1800 = √-1 × √1800 = i √1800 = 42.426i
where i = √-1 and it is called the imaginary unit.

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