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.

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

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.

☛ Check: Square Root Calculator ### Value of √1800 by Long Division Method

Explanation:

Forming pairs: 18 and 00Find a number Y (4) such that whose square is 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 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 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.

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:

Example 1: Solve the equation x2 − 1800 = 0

Solution:

x2 - 1800 = 0 i.e. x2 = 1800x = ±√1800Since the value of the square root of 1800 is 42.426,⇒ x = +√1800 or -√1800 = 42.426 or -42.426.

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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.

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### 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 = 42.426iwhere i = √-1 and it is called the imaginary unit.