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Square Root of 1234

The square root of 1234 is expressed as √1234 in the radical form and as (1234)^½ or (1234)^0.5 in the exponent form. The square root of 1234 rounded up to 6 decimal places is 35.128336. It is the positive solution of the equation x² = 1234.

Square Root of 1234: 35.12833614050059
Square Root of 1234 in exponential form: (1234)^½ or (1234)^0.5
Square Root of 1234 in radical form: √1234

Square Root of 1234

1.	What is the Square Root of 1234?
2.	How to find the Square Root of 1234?
3.	Is the Square Root of 1234 Irrational?
4.	FAQs

What is the Square Root of 1234?

The square root of 1234, (or root 1234), is the number which when multiplied by itself gives the product as 1234. Therefore, the square root of 1234 = √1234 = 35.12833614050059.

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How to Find Square Root of 1234?

Square Root of 1234 by Long Division Method

Value of √1234 by Long Division Method

Explanation:

Forming pairs: 12 and 34
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 34, to the right of the remainder 3. The new dividend is now 334.
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 5) such that 6Z × Z <= 334. After finding Z, together 6 and Z (5) form a new divisor 65 for the new dividend 334.
Divide 334 by 65 with the quotient as 5, giving the remainder = 334 - 65 × 5 = 334 - 325 = 9.
Now, let's find the decimal places after the quotient 35.
Bring down 00 to the right of this remainder 9. The new dividend is now 900.
Add the last digit of quotient to divisor i.e. 5 + 65 = 70. To the right of 70, find a digit Z (which is 1) such that 70Z × Z <= 900. Together they form a new divisor (701) for the new dividend (900).
Divide 900 by 701 with the quotient as 1, giving the remainder = 900 - 701 × 1 = 900 - 701 = 199.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 1234.

Therefore, the square root of 1234 by long division method is 35.1 approximately.

Is Square Root of 1234 Irrational?

The actual value of √1234 is undetermined. The value of √1234 up to 25 decimal places is 35.12833614050059160587031. Hence, the square root of 1234 is an irrational number.

☛ Also Check:

Square Root of 140 - √140 = 11.83216
Square Root of 25 - √25 = 5
Square Root of 85 - √85 = 9.21954
Square Root of 113 - √113 = 10.63015
Square Root of 23 - √23 = 4.79583
Square Root of 162 - √162 = 12.72792
Square Root of 90 - √90 = 9.48683

Square Root of 1234 Solved Examples

Example 1: Solve the equation x² − 1234 = 0

Solution:

x² - 1234 = 0 i.e. x² = 1234
x = ±√1234
Since the value of the square root of 1234 is 35.128,
⇒ x = +√1234 or -√1234 = 35.128 or -35.128.
Example 2: If the surface area of a cube is 7404 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 = 7404 in²
⇒ a = ±√1234 in
Since length can't be negative,
⇒ a = √1234
We know that the square root of 1234 is 35.128.
⇒ a = 35.128 in
Example 3: If the area of an equilateral triangle is 1234√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 = 1234√3 in²
⇒ a = ±√4936 in
Since length can't be negative,
⇒ a = √4936 = 2 √1234
We know that the square root of 1234 is 35.128.
⇒ a = 70.257 in

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FAQs on the Square Root of 1234

What is the Value of the Square Root of 1234?

The square root of 1234 is 35.12833.

Why is the Square Root of 1234 an Irrational Number?

Upon prime factorizing 1234 i.e. 2¹ × 617¹, 2 is in odd power. Therefore, the square root of 1234 is irrational.

Evaluate 9 plus 16 square root 1234

The given expression is 9 + 16 √1234. We know that the square root of 1234 is 35.128. Therefore, 9 + 16 √1234 = 9 + 16 × 35.128 = 9 + 562.053 = 571.053

What is the Value of 4 square root 1234?

The square root of 1234 is 35.128. Therefore, 4 √1234 = 4 × 35.128 = 140.513.

If the Square Root of 1234 is 35.128. Find the Value of the Square Root of 12.34.

Let us represent √12.34 in p/q form i.e. √(1234/100) = 12.34/10 = 3.513. Hence, the value of √12.34 = 3.513

What is the Square Root of -1234?

The square root of -1234 is an imaginary number. It can be written as √-1234 = √-1 × √1234 = i √1234 = 35.128i
where i = √-1 and it is called the imaginary unit.

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