Square Root of 325
Taking the square root of a number is raising the number to the power half which is the inverse process of squaring the number. Since 325 is not a perfect square, the square root of 325 is a decimal number and not a whole number. In this mini lesson, let us learn about the square root of 325, find out whether the square root of 325 is rational or irrational, and see how to find the square root of 325 by long division method.
 Square Root of 325: √325 = 18.027
 Square of 325: 325^{2} = 105, 625
What Is the Square Root of 325?
 If a = b^{2}, then √a = b, where a and b are natural numbers. √a is the square root of a and it is expressed in the exponential form as a^{½ }
 √325 = √(number × number (a × a)).
 √325 = (18.027× 18.027) or ( 18.027 × 18.027) ⇒ √325 = ±18.027
Is Square Root of 325 Rational or Irrational?
Irrational numbers are the real numbers that cannot be expressed as the ratio of two integers. √325 = 18.02775637731995 and hence the square root of 325 is an irrational number where the numbers after the decimal point go up to infinity.
How to Find the Square Root of 325?
The square root of 325 or any number can be calculated in many ways. Two of them are the prime factorization method and the long division method.
Square Root of 325 in its Simplest Radical Form
The square root of 325 is expressed in the radical form as √325. This can be simplified using the prime factorization. Let us express 325 as a product of its prime factors. 325 = 5 × 5 × 13. We can express √325 = √(5 × 5 × 13).
√325 = 5√13
Square Root of 325 by the Long Division Method
The long division method helps us to find a more accurate value of square root of any number. The following are the steps to evaluate the square root of 325 by the long division method.
 Step 1: Write 325.000000. Take the number in pairs from the right. 3 stands alone. Now divide 3 by a number such that (number × number) gives ≤ 1.
 Obtain quotient = 1 and remainder = 2. Double the quotient. We get 2. Have 20 as our new divisor. Bring down 25 for division.
 Step 2: Find a number such that (20 + that number) × that number gives the product ≤ 225. We find that 28 × 8 = 224. Subtract from 225 and get 1 as the remainder. Bring down the pair of zeros. 100 is our new divisor.
 18 is our quotient. Double it and get 36. 360 becomes the new divisor. Find a number such that (360 + the number) × number gets 100 or less than that. We cannot find such a number. Hence (360 + 0) ×0 = 0. Subtract and get 100 as the remainder and bring down the zeros. 1 00 00 becomes the new dividend. 18.0 is the quotient.
 Step 3: Double the quotient. 180 × 2 = 360. Have 3600 in the place of the new divisor. Find a number such that (3600 + that number) × number ≤ 1 00 00.
 We find 3602 × 2 = 72 04. Subtract this from 1 00 00 and get the remainder as 27 96.
 Repeat the steps until we approximate the square root to 3 decimal places. √325 = 18.027
Explore Square roots using illustrations and interactive examples:
Tips and Tricks
 The square root of 325 is closer to the perfect square 324. √324 = 18
 1 is the least number to be subtracted from 325 (325  1 = 324 = 18^{2}) and 36 is the least number to be added to 325 to make it a perfect square.(324 + 36 = 361= 19^{2})
Important Notes
 The square root of 325 is 18.027 approximated to 3 decimal places.
 The simplified form of 325 in its radical form is 5√13
 √325 is an irrational number.
Square Root of 325 Solved Examples

Example 1: Peter walks 15 feet South and 10 feet East. What is the distance he has reached from his starting point? Round it off to the nearest hundredth?
Solution:
The direction he has taken forms a right triangle. The distance covered will form the hypotenuse of this right triangle.
Using the Pythagorean theoerem, we have 15^{2 }+ 10^{2 }= (distance covered)^{2}
225 + 100 = (distance)^{2 } = 325
Distance = √325 feet = 18.027 = 18.03 feet. 
Example 2: Evaluate: √325 × √208
Solution:
√325 = √( 5 × 5 × 13) = 5√13
√208 = √( 4 × 4 × 13) = 4√13
√325 × √208 = 5√13 × 4√13
5 × √13 × 4 × √13 = 5 × 4 × √13 × √13
20 × 13 = 260
√325 × √208 = 260.
FAQs On Square Root of 325
What is the square root of 325?
The square root of 325 is √325 = 18.027.
What is the square root of 325 simplified?
5√13 is the simplest form of the square root of 325.
How to get the square root of 325?
The square root of 325 is evaluated by the long division method.
Is √325 a rational number?
No, √325 is an irrational number, because the value of √325 is not a whole number and it is a nonterminating decimal.
How to find the square root of 325 to the nearest hundredth?
The square root of 325 is evaluated using the division method and rounded off to the nearest hundredth.√325 = 18.027 ⇒ √325 = 18.03
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