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Square Root of 1249

The square root of 1249 is expressed as √1249 in the radical form and as (1249)^½ or (1249)^0.5 in the exponent form. The square root of 1249 rounded up to 10 decimal places is 35.3411940941. It is the positive solution of the equation x² = 1249.

Square Root of 1249: 35.34119409414458
Square Root of 1249 in exponential form: (1249)^½ or (1249)^0.5
Square Root of 1249 in radical form: √1249

Square Root of 1249

1.	What is the Square Root of 1249?
2.	How to find the Square Root of 1249?
3.	Is the Square Root of 1249 Irrational?
4.	FAQs

What is the Square Root of 1249?

The square root of 1249, (or root 1249), is the number which when multiplied by itself gives the product as 1249. Therefore, the square root of 1249 = √1249 = 35.34119409414458.

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How to Find Square Root of 1249?

Square Root of 1249 by Long Division Method

Value of √1249 by Long Division Method

Explanation:

Forming pairs: 12 and 49
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 49, to the right of the remainder 3. The new dividend is now 349.
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 <= 349. After finding Z, together 6 and Z (5) form a new divisor 65 for the new dividend 349.
Divide 349 by 65 with the quotient as 5, giving the remainder = 349 - 65 × 5 = 349 - 325 = 24.
Now, let's find the decimal places after the quotient 35.
Bring down 00 to the right of this remainder 24. The new dividend is now 2400.
Add the last digit of quotient to divisor i.e. 5 + 65 = 70. To the right of 70, find a digit Z (which is 3) such that 70Z × Z <= 2400. Together they form a new divisor (703) for the new dividend (2400).
Divide 2400 by 703 with the quotient as 3, giving the remainder = 2400 - 703 × 3 = 2400 - 2109 = 291.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 1249.

Therefore, the square root of 1249 by long division method is 35.3 approximately.

Is Square Root of 1249 Irrational?

The actual value of √1249 is undetermined. The value of √1249 up to 25 decimal places is 35.34119409414458367106665. Hence, the square root of 1249 is an irrational number.

☛ Also Check:

Square Root of 50 - √50 = 7.07107
Square Root of 37 - √37 = 6.08276
Square Root of 36 - √36 = 6
Square Root of 1000 - √1000 = 31.62278
Square Root of 63 - √63 = 7.93725
Square Root of 200 - √200 = 14.14214
Square Root of 162 - √162 = 12.72792

Square Root of 1249 Solved Examples

Example 1: Solve the equation x² − 1249 = 0

Solution:

x² - 1249 = 0 i.e. x² = 1249
x = ±√1249
Since the value of the square root of 1249 is 35.341,
⇒ x = +√1249 or -√1249 = 35.341 or -35.341.
Example 2: If the area of an equilateral triangle is 1249√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 = 1249√3 in²
⇒ a = ±√4996 in
Since length can't be negative,
⇒ a = √4996 = 2 √1249
We know that the square root of 1249 is 35.341.
⇒ a = 70.682 in
Example 3: If the surface area of a cube is 7494 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 = 7494 in²
⇒ a = ±√1249 in
Since length can't be negative,
⇒ a = √1249
We know that the square root of 1249 is 35.341.
⇒ a = 35.341 in

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FAQs on the Square Root of 1249

What is the Value of the Square Root of 1249?

The square root of 1249 is 35.34119.

Why is the Square Root of 1249 an Irrational Number?

The number 1249 is prime. This implies that the number 1249 is pairless and is not in the power of 2. Therefore, the square root of 1249 is irrational.

What is the Square Root of 1249 in Simplest Radical Form?

The number 1249 is a prime number. This implies that the number 1249 is pairless and is not in the power of 2. Therefore, the radical form of square root of 1249 cannot be simplified further.

Is the number 1249 a Perfect Square?

The number 1249 is prime. This implies that the square root of 1249 cannot be expressed as a product of two equal integers. Therefore, the number 1249 is not a perfect square.

What is the Square Root of -1249?

The square root of -1249 is an imaginary number. It can be written as √-1249 = √-1 × √1249 = i √1249 = 35.341i
where i = √-1 and it is called the imaginary unit.

What is the Square of the Square Root of 1249?

The square of the square root of 1249 is the number 1249 itself i.e. (√1249)² = (1249)^2/2 = 1249.

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