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Square Root of 100 + Solution With Free Steps

Let us find out the square root of the number 100. The number 100 is an even number, an even number is defined as a number that is perfectly divisible by 2 also we see whether 100 is a perfect square number or not.

In this article, we will analyze and find the square root of 100 using various mathematical techniques, such as the approximation method and the long division method.

What Is the Square Root Of 100?

The square root of the number 100 is 10.

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:

√100 = √(10 x 10)

√100 = √(10)$^2$

√100 = ±10

The square can be canceled with the square root as it is equivalent to 1/2; therefore, obtaining 10. Hence 10 is 100’s square root. The square root generates both positive and negative integers.

How To Calculate the Square Root of 100?

You can calculate the square root of 100 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 100 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 100 using the long division method:

Step 1

First, write the given number 100 in the division symbol, as shown in figure 1.

Step 2

Starting from the right side of the number, divide the number 100 into pairs such as 00 and 1.

Step 3

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

Step 4

After this, bring down the next pair 00. Now the dividend is 00. 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 $\leq$ 00 when multiplied with the divisor. 

Step 6

Adding 0 to the divisor and multiplying 20 with 0 results in 0 $\leq$ 0. The remainder obtained is 0, and the quotient is also 0.

Step 7

The resulting quotient 10 is the square root of 100. Figure 1 given below shows the long division process in detail:

Square root of 100 figure 1

Important points

  • The number X is a perfect square/ not a perfect square.
  • The number X is a rational number/ irrational number.
  • The number X can be split into its prime factorization.

Is Square Root of 100 a Perfect Square?

The number 100 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 100 is concerned, it is a perfect square. It can be proved as below:

 

Factorization of 100 results in 10 x 10 which can also be expressed as 10$^2$.

Taking the square root of the above expression gives:

= √(10$^2$)

= (10$^2$)$^{1/2}$

= 10

This shows that 100 is a perfect square and a rational number.

Therefore the above discussion proves that the square root of 100 is equivalent to 10.

Images/mathematical drawings are created with GeoGebra.

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