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Square Root of 1200

The square root of 1200 is expressed as √1200 in the radical form and as (1200)^½ or (1200)^0.5 in the exponent form. The square root of 1200 rounded up to 6 decimal places is 34.641016. It is the positive solution of the equation x² = 1200. We can express the square root of 1200 in its lowest radical form as 20 √3.

Square Root of 1200: 34.64101615137755
Square Root of 1200 in exponential form: (1200)^½ or (1200)^0.5
Square Root of 1200 in radical form: √1200 or 20 √3

Square Root of 1200

1.	What is the Square Root of 1200?
2.	How to find the Square Root of 1200?
3.	Is the Square Root of 1200 Irrational?
4.	FAQs

What is the Square Root of 1200?

The square root of 1200, (or root 1200), is the number which when multiplied by itself gives the product as 1200. Therefore, the square root of 1200 = √1200 = 20 √3 = 34.64101615137755.

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How to Find Square Root of 1200?

Square Root of 1200 by Long Division Method

Value of √1200 by Long Division Method

Explanation:

Forming pairs: 12 and 00
Find a number Y (3) such that whose square is <= 12. Now divide 12 by 3 with quotient as 3.
Bring down the next pair 00, to the right of the remainder 3. The new dividend is now 300.
Add the last digit of the quotient (3) to the divisor (3) i.e. 3 + 3 = 6. To the right of 6, find a digit Z (which is 4) such that 6Z × Z <= 300. After finding Z, together 6 and Z (4) form a new divisor 64 for the new dividend 300.
Divide 300 by 64 with the quotient as 4, giving the remainder = 300 - 64 × 4 = 300 - 256 = 44.
Now, let's find the decimal places after the quotient 34.
Bring down 00 to the right of this remainder 44. The new dividend is now 4400.
Add the last digit of quotient to divisor i.e. 4 + 64 = 68. To the right of 68, find a digit Z (which is 6) such that 68Z × Z <= 4400. Together they form a new divisor (686) for the new dividend (4400).
Divide 4400 by 686 with the quotient as 6, giving the remainder = 4400 - 686 × 6 = 4400 - 4116 = 284.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 1200.

Therefore, the square root of 1200 by long division method is 34.6 approx.

Is Square Root of 1200 Irrational?

The actual value of √1200 is undetermined. The value of √1200 up to 25 decimal places is 34.64101615137754587054893. Hence, the square root of 1200 is an irrational number.

☛ Also Check:

Square Root of 125 - √125 = 11.18034
Square Root of 80 - √80 = 8.94427
Square Root of 97 - √97 = 9.84886
Square Root of 192 - √192 = 13.85641
Square Root of 69 - √69 = 8.30662
Square Root of 149 - √149 = 12.20656
Square Root of 140 - √140 = 11.83216

Square Root of 1200 Solved Examples

Example 1: Solve the equation x² − 1200 = 0

Solution:

x² - 1200 = 0 i.e. x² = 1200
x = ±√1200
Since the value of the square root of 1200 is 34.641,
⇒ x = +√1200 or -√1200 = 34.641 or -34.641.
Example 2: If the surface area of a cube is 7200 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 = 7200 in²
⇒ a = ±√1200 in
Since length can't be negative,
⇒ a = √1200
We know that the square root of 1200 is 34.641.
⇒ a = 34.641 in
Example 3: If the surface area of a sphere is 4800π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 4800π in²
⇒ r = ±√1200 in
Since radius can't be negative,
⇒ r = √1200
The square root of 1200 is 34.641.
⇒ r = 34.641 in

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FAQs on the Square Root of 1200

What is the Value of the Square Root of 1200?

The square root of 1200 is 34.64101.

Why is the Square Root of 1200 an Irrational Number?

Upon prime factorizing 1200 i.e. 2⁴ × 3¹ × 5², 3 is in odd power. Therefore, the square root of 1200 is irrational.

What is the Square Root of -1200?

The square root of -1200 is an imaginary number. It can be written as √-1200 = √-1 × √1200 = i √1200 = 34.641i
where i = √-1 and it is called the imaginary unit.

What is the Square Root of 1200 in Simplest Radical Form?

We need to express 1200 as the product of its prime factors i.e. 1200 = 2 × 2 × 2 × 2 × 3 × 5 × 5. Therefore, √1200 = √2 × 2 × 2 × 2 × 3 × 5 × 5 = 20 √3. Thus, the square root of 1200 in the lowest radical form is 20 √3.

Evaluate 2 plus 17 square root 1200

The given expression is 2 + 17 √1200. We know that the square root of 1200 is 34.641. Therefore, 2 + 17 √1200 = 2 + 17 × 34.641 = 2 + 588.897 = 590.897

Is the number 1200 a Perfect Square?

The prime factorization of 1200 = 2⁴ × 3¹ × 5². Here, the prime factor 3 is not in the pair. Therefore, 1200 is not a perfect square.

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