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# What Is The Square Root Of 225? How to Find the Square Root of 225?

What is the square root of 225? The Square Root of 225 is an rational number.

It can be expressed as a natural number

We are going to use algebraic notation and the fundamental theorem of arithmetic to prove this statement true. Be sure you have a piece of paper handy because there will be some writing involved! Let’s get started…

## What is the square root of 225?

The square root of 225 is expressed as √225. The square root of 225 is 15. In other words, √225 = 15.

## Is the Square Root of 225 Rational or Irrational?

The Square Root of 225 can be expressed as the ratio of two integers (15/1). So the Square Root of 225 is Rational.

## How to Find the Square Root of 225?

### Square Root of 225 by Prime Factorization

This problem requires the prime factorization of a number, which can be done by either using a ladder or tree formula.

The first step in both formulas is to divide into each other until one divides no longer gives an remainder when divided again (the factors). After this process has been repeated n times with 2 taken as input;

if we get back quotienty dividable only by remaining fractional part then our final answer will also have that property and therefore prove accurate enough for us seeking =to find its square root value sqrt(225)=√(5 × 5 × 3 × 3)

Squaring on both the sides, we get, √225 =√(52 × 32)

=> this give us 5x 3 = 13

### Square Root of 225 by Long Division Method

Here are the steps to find the square root of 225

Step 1: Write the pair of digits starting from one’s place. It is 25.

Step 2: Finding a divisor “n” so that n × n results ≤ 2. We find 1 × 1 = 1, follow the process of long division and obtain the remainder.

Step 3: Now, bring down the next pair of numbers. Here it’s 25. Multiply the quotient 1 with 2 and write it in the new divisor’s place. We have the 2.

Step 4: Find a divisor “n” such that n × n results in the product ≤ 125. Get the next quotient place as 5. Now we get our new divisor as 25, as 5 × 125 = 225.

Step 5: Divide and get remainder, So we have 0. Therefore, 15 is the Square Root of 225.

## Square Root of 225 Solved Examples

### Mark’s backyard is 225 square feet. How many feet of fencing will Mark need to?

Area = Side × Side = 225 (sq feet)

=> 15 × 15 = 225

Each side will be = 15 feet

=> Mark need to fence 4 x 15 = 60 sq feet

### If the area of a circle is 225π in2. Find the radius of the circle.

Area of the circle = πr2 = 225π in2

⇒ r = √225 = 15 in

## FAQ

### What is 225 square root simplified?

The simplified notation for the square root of 225 is 15.

### What is the perfect square of 225?

The perfect square of 225 is found by taking the square root of the two-digit number 225, which is 15.

### IS 225 a perfect cube or square?

225 is not a perfect square or cube. Square numbers are always of the form n², and cubes are always of the form n³.

### IS 200 a perfect square?

200 is a perfect square because it is an even, natural number and takes the form n².

### What is 256 the square root of?

The square root of 256 is 16.

## Conclusion

We can prove that both 3 and – √9 are rational numbers. The other two roots of 9, ∛3 and ∛-(3 × 3) are irrational numbers. That is because the number 9 has no prime factors to simplify it as a fraction with an infinite number of digits behind the decimal point.

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