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Square Root of 3250

The square root of 3250 is expressed as √3250 in the radical form and as (3250)^½ or (3250)^0.5 in the exponent form. The square root of 3250 rounded up to 7 decimal places is 57.0087713. It is the positive solution of the equation x² = 3250. We can express the square root of 3250 in its lowest radical form as 5 √130.

Square Root of 3250: 57.0087712549569
Square Root of 3250 in exponential form: (3250)^½ or (3250)^0.5
Square Root of 3250 in radical form: √3250 or 5 √130

Square Root of 3250

1.	What is the Square Root of 3250?
2.	How to find the Square Root of 3250?
3.	Is the Square Root of 3250 Irrational?
4.	FAQs

What is the Square Root of 3250?

The square root of 3250, (or root 3250), is the number which when multiplied by itself gives the product as 3250. Therefore, the square root of 3250 = √3250 = 5 √130 = 57.0087712549569.

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How to Find Square Root of 3250?

Square Root of 3250 by Long Division Method

Value of √3250 by Long Division Method

Explanation:

Forming pairs: 32 and 50
Find a number Y (5) such that whose square is <= 32. Now divide 32 by 5 with quotient as 5.
Bring down the next pair 50, to the right of the remainder 7. The new dividend is now 750.
Add the last digit of the quotient (5) to the divisor (5) i.e. 5 + 5 = 10. To the right of 10, find a digit Z (which is 7) such that 10Z × Z <= 750. After finding Z, together 10 and Z (7) form a new divisor 107 for the new dividend 750.
Divide 750 by 107 with the quotient as 7, giving the remainder = 750 - 107 × 7 = 750 - 749 = 1.
Now, let's find the decimal places after the quotient 57.
Bring down 00 to the right of this remainder 1. The new dividend is now 100.
Add the last digit of quotient to divisor i.e. 7 + 107 = 114. To the right of 114, find a digit Z (which is 0) such that 114Z × Z <= 100. Together they form a new divisor (1140) for the new dividend (100).
Divide 100 by 1140 with the quotient as 0, giving the remainder = 100 - 1140 × 0 = 100 - 0 = 100.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 3250.

Therefore, the square root of 3250 by long division method is 57.0 approximately.

Is Square Root of 3250 Irrational?

The actual value of √3250 is undetermined. The value of √3250 up to 25 decimal places is 57.00877125495689895680245. Hence, the square root of 3250 is an irrational number.

☛ Also Check:

Square Root of 17 - √17 = 4.12311
Square Root of 51 - √51 = 7.14143
Square Root of 10 - √10 = 3.16228
Square Root of 12 - √12 = 3.46410
Square Root of 361 - √361 = 19
Square Root of 1000 - √1000 = 31.62278
Square Root of 39 - √39 = 6.24500

Square Root of 3250 Solved Examples

Example 1: Solve the equation x² − 3250 = 0

Solution:

x² - 3250 = 0 i.e. x² = 3250
x = ±√3250
Since the value of the square root of 3250 is 57.009,
⇒ x = +√3250 or -√3250 = 57.009 or -57.009.
Example 2: If the area of a circle is 3250π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 3250π in²
⇒ r = ±√3250 in
Since radius can't be negative,
⇒ r = √3250
The square root of 3250 is 57.009.
⇒ r = 57.009 in
Example 3: If the area of a square is 3250 in². Find the length of the side of the square.

Solution:

Let 'a' be the length of the side of the square.
⇒ Area of the square = a² = 3250 in²
⇒ a = ±√3250 in
Since length can't be negative,
⇒ a = √3250 = 57.009 in

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FAQs on the Square Root of 3250

What is the Value of the Square Root of 3250?

The square root of 3250 is 57.00877.

Why is the Square Root of 3250 an Irrational Number?

Upon prime factorizing 3250 i.e. 2¹ × 5³ × 13¹, 2 is in odd power. Therefore, the square root of 3250 is irrational.

What is the Square Root of 3250 in Simplest Radical Form?

We need to express 3250 as the product of its prime factors i.e. 3250 = 2 × 5 × 5 × 5 × 13. Therefore, √3250 = √2 × 5 × 5 × 5 × 13 = 5 √130. Thus, the square root of 3250 in the lowest radical form is 5 √130.

What is the Value of 1 square root 3250?

The square root of 3250 is 57.009. Therefore, 1 √3250 = 1 × 57.009 = 57.009.

What is the Square Root of -3250?

The square root of -3250 is an imaginary number. It can be written as √-3250 = √-1 × √3250 = i √3250 = 57.008i
where i = √-1 and it is called the imaginary unit.

Evaluate 10 plus 17 square root 3250

The given expression is 10 + 17 √3250. We know that the square root of 3250 is 57.009. Therefore, 10 + 17 √3250 = 10 + 17 × 57.009 = 10 + 969.149 = 979.149

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