Square Root of 49

In Mathematics, the square root of 49 is defined as a number, which on multiplication by itself for two times, results in the original number 49. The value of the square root of 49 is a rational number since it can be represented in the form of p/q. In this article, we will learn two different such as the long division method and the prime factorization method to determine the square root of 49 with complete explanation.

What is the Value of Square Root of 49?

If a number is multiplied by itself and gives the result as 49, then we can say that the number is the square root 49. Symbolically, the square root of 49 is expressed as √49.

Hence, √49 = √(Number × Number)

Hence, by multiplying the number 7 for two times, we get the original number 49.

(i.e) √49 = √(7× 7)

√49 = √(7)²

On removing square and square root, we will get

√49 = ± 7

Similarly, the simplest radical form of square root of 49 is √49.

Square Root of 49 by Prime Factorization Method

The square root of 49 can be found using the prime factorization method. To find the value, we should know the prime factorization of 49. Thus, the prime factorization of a number 49 is 7×7.

Thus, √49 = √(7×7)

√49 = (√7)²

√49 = 7

Hence, the square root of 49 is equal to 7.

Square Root of 49 by Long Division Method

The steps to obtain the square root of 49 using the long division method is provided as follows:

Step 1: First, write the number 49. Next, Pair the number 49 by putting the bar on the top of the number from right to left.

Step 2: Next, divide a number 49 by a number, such that the multiplication of the same number must be less than or equal to 49. Hence, 7×7=49, which is equal to 49.

Step 3: Thus, we get quotient = 7 and remainder = 0.

Step 4: Therefore, the value of the square root of 49, √49 is 7.

Video Lessons on Square Roots

Visualising square roots

Finding Square roots

Examples

Example 1:

Simplify: 7√49 + 5√49

Solution:

Given: 7√49 + 5√49

As we know that the square root of 49 is 7.

Substituting the value in the expression,

7√49 + 5√49= 12√49

7√49 + 5√49 = 12(7)= 84

Therefore, the simplification of 7√49 + 5√49 is 84.

Example 2:

Find the value of p, if p√49 = 21.

Solution:

Given: p√49 = 21…(1)

We know that √49 = 7

Now, substitute the value in equation (1), we get

p(7) = 21

p = 21/7 = 3.

Hence, the value of p is 3.

Example 3:

What is the value of 10√49 + 7?

Solution:

Given expression: 10√49 + 7.

We know that √49 is 7.

Hence, 10√49 + 7 = 10(7) + 7

= 70+7

= 77.

Therefore, the value of 10√49 + 7 = 77.