Square Root of 225 + Solution With Free Steps

The square root of the number 225 is 15, making it a perfect square as 15 is an integer. Mathematically, we can write it as √225 = 15. The square root of 225 equal to 15 is a rational number, which means it is a ratio of two integers.In this article, we will analyze and find the square root of 225 using various mathematical techniques, such as the approximation method and the long division method.

What Is the Square Root Of 225?

The square root of the number 225 is 15.The square root can be defined as the quantity that can be doubled to produce the square of that similar quantity. In simple words, it can be explained as:

√225 = √(15 x 15)

√225 = √(15)$^2$

√225 = ±15

The square can be canceled with the square root as it is equivalent to 1/2; therefore, obtaining 15. Hence 15 is 225’s square root. The square root generates both positive and negative integers.

How To Calculate the Square Root of 225?

You can calculate the square root of 225 using any of two vastly used techniques in mathematics; one is the Approximation technique, and the other is the Long Division method.The symbol √ is interpreted as 225 raised to the power 1/2. So any number, when multiplied by itself, produces its square, and when the square root of any squared number is taken, it produces the actual number.Let us discuss each of them to understand the concepts better.

Square Root by Long Division Method

The process of long division is one of the most common methods used to find the square roots of a given number. It is easy to comprehend and provides more reliable and accurate answers. The long division method reduces a multi-digit number to its equal parts.Learning how to find the square root of a number is easy with the long division method. All you need are five primary operations- divide, multiply, subtract, bring down or raise, then repeat.Following are the simple steps that must be followed to find the square root of 225 using the long division method:

Step 1

First, write the number 225 in the division symbol, as shown in figure 1.

Step 2

Starting from the right side of the number, divide the number 225 into pairs such as 25 and 2.

Step 3

Now divide the digit 25 by a number, giving a number either 25 or less than 25. Therefore, in this case, the remainder is 1, whereas the quotient is 1.

Step 4

After this, bring down the next pair, 25. Now the dividend is 125. To find the next divisor, we need to double our quotient obtained before. Doubling 1 gives 2; hence consider it as the next divisor.

Step 5

Now pair 2 with another number to make a new divisor that results in $\leq$ 125 when multiplied with the divisor.

Step 6

Adding 5 to the divisor and multiplying 25 with 5 results in 125 $\leq$ 125. The remainder obtained is 0.

Step 7

The resulting quotient 15  is the square root of 225. Figure 1 given below shows the long division process in detail:

Important points

• The number 225 is a perfect square.
• The number 225  is rational.
• The number 225 can be split into its prime factorization.

Is Square Root of 225 a Perfect Square?

The number 225 is a perfect square. A number is a perfect square if it splits into two equal parts or identical whole numbers. If a number is a perfect square, it is also rational.A number expressed in p/q form is called a rational number. All the natural numbers are rational. A square root of a perfect square is a whole number; therefore, a perfect square is a rational number.A number that is not a perfect square is irrational as it is a decimal number. As far as 225 is concerned, it is a perfect square. It can be proved as below:Factorization of 225 results in 15 x 15, which can also be expressed as 15$^2$.Taking the square root of the above expression gives:

= √(15$^2$)

= (15$^2$)$^{1/2}$

= 15

This shows that 225 is a perfect square and a rational number.Therefore the above discussion proves that the square root of 225 is equivalent to 15.Images/mathematical drawings are created with GeoGebra.

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