Square Root of 7 is approximately 2.646. Since 7 is a prime number, its exact value cannot be expressed. When multiplied by itself, the square root of 7, i.e., 2.646, yields 7.001, nearly equal to 7. In this article, we will discuss all the methods for the calculation of the square of root 7.

Value of Square Root of 7

Value of Square Root of 7 is approximatly 2. 645 and is expressed as √7. Square Root of Root 7 when the number “2.645” is multiplied by the number itself, that gives the result of √7. Suppose, the number is 2.645 that multiplied twice “2.645 × 2.645” then we get the number 7. A square root of 7 can be represented as follows:

√7 = 2.645

OR

(7)^1/2 = 2.645

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Square Root of 7 Calculator

How to Calculate Square Root of 7?

Some of the methods are given below to find out the square root of 7.

• Square Root of 7 by Long Division Method
• Square Root of 7 by Estimation Method

Square Root of 7 by Long Division Method

The long division method is used to find the square root of 7 because it is not a perfect square integer. So, let’s find out the value of √7 in the following steps that are given below;

• Let’s begin with the value √7.
• After that, the square root makes a realistic estimate first. Since 2² = 4, 2 is an excellent starting point for 7.
• After multiplying the divisor (2) by itself, deduct the outcome from 7. Thus 2 × 2 = 4, which is smaller than 7.
• Then, subtract 4 from 7, we will get the remainder of 3 and quotient 2.
• As we now have 4 after doubling the quotient, we can assume that 40 is the new divisor.
• Now, bring two zeroes down that give 300 as our new dividend.
• Then find the number, As (40+ new number) × new number [Getting number should be less than or equal to 300.]
  Hence, (40+6) × 6 = 276.
  Therefore, 276 < 300.
• Again, subtract 276 from 300 which will give a remainder of 24 and the quotient is 26.
• Continue with this until the square root of 7 is obtained to three decimal places.
• Therefore, in the end, the value of the square root of 7 is approximately equal to 2.645.

Above steps can be represented as follows:

Read More about Square Root by Long Division.

Square Root 7 by Estimation Method

To get closer to the real value, we first estimate the square root of 7 using the estimation method. Some of the steps are given below;

• Let’s start with 2, and multiply it two times (2 × 2 = 4).
• Now, compare the result 4 with 7. Therefore, 4 is less than 7, we need a larger estimate.
• Now, the estimated number should be 3, multiple it two times (3 × 3 = 9).
• Then, compare the result 9 with 7. Therefore, 9 is more than 7, so we need a smaller estimate.
• Now, the number should be taken between 2 and 3 which should be 2.5.
• At last, the estimated number should be 2.5, multiple it two times (2.5 × 2.5 = 6.25), 6.25 is still less than 7.
• Therefore, this process can’t be ended here only, that should be continued for a long until you get the approximate value of the square root of 7.

Is Square Root of 7 Rational or Irrational?

The square root of 7 is an irrational number. Let’s assume it is in value of √7 that can be expressed in the form of a quotient or division of two integers, i.e. p/q, where q is not equal to 0. Therefore, √7  = 2.645751311064591 and due to its never-ending process after the decimal point that is why it’s an irrational number.

Conclusion

In conclusion, the square root of 7 is an irrational number that represents the length of one side of a square with an area of 7 square units and its value is approximatly 2.645. While it cannot be expressed as a simple fraction, its decimal representation goes on indefinitely without repeating.

Read More,

• Square Root Formula
• Square Root of 72

Square Root of 7: FAQs

What is the Square Root Value of 7?

The square root of 7 is approximately equals to 2.6457.

What is Square of 7?

The square of 7 can be written as 7² and is equals to 49.

What is the Symbol for Root?

Symbol for square root is √.

 Is 7 a Perfect Square?

No, 7 is not a perfect square as 7 is a prime number.

Why is the Square Root of 7 an Irrational Number?

The square root of 7 is irrational because it cannot be expressed as a simple fraction, and its decimal representation is non-repeating and non-terminating.