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Square Root of 1224

The square root of 1224 is expressed as √1224 in the radical form and as (1224)^½ or (1224)^0.5 in the exponent form. The square root of 1224 rounded up to 10 decimal places is 34.9857113691. It is the positive solution of the equation x² = 1224. We can express the square root of 1224 in its lowest radical form as 6 √34.

Square Root of 1224: 34.9857113690718
Square Root of 1224 in exponential form: (1224)^½ or (1224)^0.5
Square Root of 1224 in radical form: √1224 or 6 √34

Square Root of 1224

1.	What is the Square Root of 1224?
2.	How to find the Square Root of 1224?
3.	Is the Square Root of 1224 Irrational?
4.	FAQs

What is the Square Root of 1224?

The square root of 1224, (or root 1224), is the number which when multiplied by itself gives the product as 1224. Therefore, the square root of 1224 = √1224 = 6 √34 = 34.9857113690718.

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How to Find Square Root of 1224?

Square Root of 1224 by Long Division Method

Value of √1224 by Long Division Method

Explanation:

Forming pairs: 12 and 24
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 24, to the right of the remainder 3. The new dividend is now 324.
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 <= 324. After finding Z, together 6 and Z (4) form a new divisor 64 for the new dividend 324.
Divide 324 by 64 with the quotient as 4, giving the remainder = 324 - 64 × 4 = 324 - 256 = 68.
Now, let's find the decimal places after the quotient 34.
Bring down 00 to the right of this remainder 68. The new dividend is now 6800.
Add the last digit of quotient to divisor i.e. 4 + 64 = 68. To the right of 68, find a digit Z (which is 9) such that 68Z × Z <= 6800. Together they form a new divisor (689) for the new dividend (6800).
Divide 6800 by 689 with the quotient as 9, giving the remainder = 6800 - 689 × 9 = 6800 - 6201 = 599.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 1224.

Therefore, the square root of 1224 by long division method is 34.9 approx.

Is Square Root of 1224 Irrational?

The actual value of √1224 is undetermined. The value of √1224 up to 25 decimal places is 34.98571136907180282524492. Hence, the square root of 1224 is an irrational number.

☛ Also Check:

Square Root of 22 - √22 = 4.69042
Square Root of 23 - √23 = 4.79583
Square Root of 74 - √74 = 8.60233
Square Root of 72 - √72 = 8.48528
Square Root of 200 - √200 = 14.14214
Square Root of 76 - √76 = 8.71780
Square Root of 27 - √27 = 5.19615

Square Root of 1224 Solved Examples

Example 1: Solve the equation x² − 1224 = 0

Solution:

x² - 1224 = 0 i.e. x² = 1224
x = ±√1224
Since the value of the square root of 1224 is 34.986,
⇒ x = +√1224 or -√1224 = 34.986 or -34.986.
Example 2: If the area of a circle is 1224π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 1224π in²
⇒ r = ±√1224 in
Since radius can't be negative,
⇒ r = √1224
The square root of 1224 is 34.986.
⇒ r = 34.986 in
Example 3: If the surface area of a sphere is 4896π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 4896π in²
⇒ r = ±√1224 in
Since radius can't be negative,
⇒ r = √1224
The square root of 1224 is 34.986.
⇒ r = 34.986 in

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FAQs on the Square Root of 1224

What is the Value of the Square Root of 1224?

The square root of 1224 is 34.98571.

Why is the Square Root of 1224 an Irrational Number?

Upon prime factorizing 1224 i.e. 2³ × 3² × 17¹, 2 is in odd power. Therefore, the square root of 1224 is irrational.

What is the Square Root of -1224?

The square root of -1224 is an imaginary number. It can be written as √-1224 = √-1 × √1224 = i √1224 = 34.985i
where i = √-1 and it is called the imaginary unit.

What is the Square of the Square Root of 1224?

The square of the square root of 1224 is the number 1224 itself i.e. (√1224)² = (1224)^2/2 = 1224.

If the Square Root of 1224 is 34.986. Find the Value of the Square Root of 12.24.

Let us represent √12.24 in p/q form i.e. √(1224/100) = 12.24/10 = 3.499. Hence, the value of √12.24 = 3.499

What is the Square Root of 1224 in Simplest Radical Form?

We need to express 1224 as the product of its prime factors i.e. 1224 = 2 × 2 × 2 × 3 × 3 × 17. Therefore, √1224 = √2 × 2 × 2 × 3 × 3 × 17 = 6 √34. Thus, the square root of 1224 in the lowest radical form is 6 √34.

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