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Square Root of 49 + Solution With Free Steps

The square root of a number 49 is 7  i.e. when we multiply 7 by itself it gives 49. This can also be written as √49=7 or 7$^2$=49. The number 49 is a perfect square as the result of √49 is an integer 7.

In this article, we will analyze and find the square root of 49 using various mathematical techniques, such as the approximation method and the long division method.

What Is the Square Root Of 49?

The square root of the number 49 is 7.

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:

√49 = √(7 x 7)

√49 = √(7)$^2$

√49 = ±7

The square can be canceled with the square root as it is equivalent to 1/2; therefore, obtaining 7. Hence 7 is 49’s square root. The square root generates both positive and negative integers.

How To Calculate the Square Root of 49?

You can calculate the square root of 49 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 49 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 49 using the long division method:

Step 1

First, write the given number 49 in the division symbol, as shown in figure 1.

Step 2

Starting from the right side of the number, divide the number 49 into pairs such as 49.

Step 3

Now divide the digit 49 by a number, giving a number either 49 or less than 49. Therefore, in this case, the remainder is zero, whereas the quotient is 7.

Step 4

The resulting quotient 7 is the square root of 49. Figure 1 given below shows the long division process in detail:

Important points

  • The number 49 is a perfect square.
  • The number 49 is a rational number.
  • The number 49 can be split into its prime factorization.

Is Square Root of 49 a Perfect Square?

The number 49 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 49 is concerned, it is a perfect square. It can be proved as below:

Factorization of 49 results in 7 x 7 that can also be expressed as 7$^2$.

Taking the square root of the above expression gives:

= √(7$^2$)

= (7$^2$)$^{1/2}$

= 7

This shows that 49 is a perfect square and a rational number.

Therefore the above discussion proves that the square root of 49 is equivalent to 7.

Images/mathematical drawings are created with GeoGebra.

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