Root 7 – Value, Meaning and examples

Just like finding values of other square roots, you need to know whether a number is a perfect square or not. In this article, we will learn how to find the value of the square root of 7. We know that mathematics is all about playing with numbers, and finding the square root is easy if you are aware of simple maths skills. However, before jumping in, you must know that you can find the value of √7.

Value of root 7

It is necessary to know what are perfect and non-perfect squares before determining the value of root 7. In the ones place of any perfect square integer, there are 1, 4, 5, 6, 9. Every number ending with 2, 3, 7 and 8 are referred to as non-perfect. Therefore, 7 is a non-perfect square, and √7 is equal to 2.64575 (rounded up to 5 decimal places). This also indicates that (2.64575)^{2}= 7. Although root 7 can have a negative value as well, in this article, we will only consider the positive value.

√7 is an irrational number

How do you differentiate between a rational and an irrational number? While we know that we can express a rational number in the form of \frac{p}{q} where q ≠ 0. , An irrational number cannot be expressed in this way. Any number that does not seem to terminate after the decimal point is called an irrational number. In this case, √7 is an irrational number because its value, 2.645751311064591, doesn’t terminate after the decimal, and it is a never-ending number.

Finding the value of √7 by the average method

1. Before you dive in with numbers, know that the square root of 7 would lie somewhere between the square root of two perfect square numbers.

2. Find the two perfect squares before and after √7, i.e., √4 and √9 as √4 < √7 < √9.

3. Therefore, the value of √7 lies between 2 and 3.

4. Now divide 7 with either 2 or 3. Here, we decided to divide 7 by 3, thereby,

7 ÷ 3 = 2.33

5. Calculate the average of 2.33 and 3.

(2.33+3) ÷ 2 = 2.66

6. Therefore, by using the average method, we get an approximate value of √7 as 2.66

√7 by long division method

The long division method is the most widely accepted method to find the value of a square root. It not only gives the exact value of a square root but also helps you form a better understanding of numbers.

Follow the steps below to find the value of √7 by long division method:

Begin to pair numbers- right to left for whole numbers and left to right for decimal numbers

Step 1: Write 7, put a decimal point after it and place 3 pairs of zeros after the decimal point.

Step 2: Now group these zeros into pairs of two by placing a bar above each pair.

Step 3: Choose a number whose square gives a value below 7. In this case, the number is 2 as (2)^{2}=4. So write 2 in the dividend and quotient place. Now, follow the traditional way of division.

Step 4: Now, bring down the pair of zeros and place the decimal in the quotient, after 2.

Step 5: Add 2 to the divisor to get 4, and now think of a number to make a two-digit number which, when multiplied by the number taken, gives a number smaller than the current dividend.

Step 6: Repeat the above steps, until you get the quotient value up to 3 decimal places.
The value of √7 = 2.645

Examples

Question 1: Find the value of ‘x’ if x^{2}=28.

Solution: Given, x^{2}=28.

x = √28

x = (√4 x √7)

We know that √4 = 2

so, x = 2 (√7)

x = 2 x 2.645

x = 5.29

Question 2: Calculate the radius of circular cardboard if its area is 22 \mathrm{~cm}^{2}.

Solution: We know that \pi r^{2}gives the area of a circle. 

Given, area =22 \mathrm{~cm}^{2}

so, \pi r^{2}=22

\Rightarrow \frac{22}{7}\times r^{2}=22

\Rightarrow r^{2}=7

Hence, r = √7 = 2.645 cm (rounded up to 3 decimal places)

Therefore, the radius of the circular cardboard is 2.645cm.