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Square Root of 1250

The square root of 1250 is expressed as √1250 in the radical form and as (1250)^½ or (1250)^0.5 in the exponent form. The square root of 1250 rounded up to 10 decimal places is 35.3553390593. It is the positive solution of the equation x² = 1250. We can express the square root of 1250 in its lowest radical form as 25 √2.

Square Root of 1250: 35.35533905932738
Square Root of 1250 in exponential form: (1250)^½ or (1250)^0.5
Square Root of 1250 in radical form: √1250 or 25 √2

Square Root of 1250

1.	What is the Square Root of 1250?
2.	How to find the Square Root of 1250?
3.	Is the Square Root of 1250 Irrational?
4.	FAQs

What is the Square Root of 1250?

The square root of 1250, (or root 1250), is the number which when multiplied by itself gives the product as 1250. Therefore, the square root of 1250 = √1250 = 25 √2 = 35.35533905932738.

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How to Find Square Root of 1250?

Square Root of 1250 by Long Division Method

Value of √1250 by Long Division Method

Explanation:

Forming pairs: 12 and 50
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 50, to the right of the remainder 3. The new dividend is now 350.
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 <= 350. After finding Z, together 6 and Z (5) form a new divisor 65 for the new dividend 350.
Divide 350 by 65 with the quotient as 5, giving the remainder = 350 - 65 × 5 = 350 - 325 = 25.
Now, let's find the decimal places after the quotient 35.
Bring down 00 to the right of this remainder 25. The new dividend is now 2500.
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 <= 2500. Together they form a new divisor (703) for the new dividend (2500).
Divide 2500 by 703 with the quotient as 3, giving the remainder = 2500 - 703 × 3 = 2500 - 2109 = 391.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 1250.

Therefore, the square root of 1250 by long division method is 35.3 approx.

Is Square Root of 1250 Irrational?

The actual value of √1250 is undetermined. The value of √1250 up to 25 decimal places is 35.35533905932737622004222. Hence, the square root of 1250 is an irrational number.

☛ Also Check:

Square Root of 1000 - √1000 = 31.62278
Square Root of 96 - √96 = 9.79796
Square Root of 60 - √60 = 7.74597
Square Root of 63 - √63 = 7.93725
Square Root of 325 - √325 = 18.02776
Square Root of 45 - √45 = 6.70820
Square Root of 192 - √192 = 13.85641

Square Root of 1250 Solved Examples

Example 1: Solve the equation x² − 1250 = 0

Solution:

x² - 1250 = 0 i.e. x² = 1250
x = ±√1250
Since the value of the square root of 1250 is 35.355,
⇒ x = +√1250 or -√1250 = 35.355 or -35.355.
Example 2: If the surface area of a sphere is 5000π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 5000π in²
⇒ r = ±√1250 in
Since radius can't be negative,
⇒ r = √1250
The square root of 1250 is 35.355.
⇒ r = 35.355 in
Example 3: If the surface area of a cube is 7500 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 = 7500 in²
⇒ a = ±√1250 in
Since length can't be negative,
⇒ a = √1250
We know that the square root of 1250 is 35.355.
⇒ a = 35.355 in

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FAQs on the Square Root of 1250

What is the Value of the Square Root of 1250?

The square root of 1250 is 35.35533.

Why is the Square Root of 1250 an Irrational Number?

Upon prime factorizing 1250 i.e. 2¹ × 5⁴, 2 is in odd power. Therefore, the square root of 1250 is irrational.

Evaluate 3 plus 19 square root 1250

The given expression is 3 + 19 √1250. We know that the square root of 1250 is 35.355. Therefore, 3 + 19 √1250 = 3 + 19 × 35.355 = 3 + 671.751 = 674.751

If the Square Root of 1250 is 35.355. Find the Value of the Square Root of 12.5.

Let us represent √12.5 in p/q form i.e. √(1250/100) = 12.5/10 = 3.536. Hence, the value of √12.5 = 3.536

What is the Square Root of 1250 in Simplest Radical Form?

We need to express 1250 as the product of its prime factors i.e. 1250 = 2 × 5 × 5 × 5 × 5. Therefore, √1250 = √2 × 5 × 5 × 5 × 5 = 25 √2. Thus, the square root of 1250 in the lowest radical form is 25 √2.

What is the Square Root of -1250?

The square root of -1250 is an imaginary number. It can be written as √-1250 = √-1 × √1250 = i √1250 = 35.355i
where i = √-1 and it is called the imaginary unit.

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