Square Root of 7
The square root of 7 is expressed as √7 in the radical form and as (7)^{½} or (7)^{0.5} in the exponent form. The square root of 7 rounded up to 8 decimal places is 2.64575131. It is the positive solution of the equation x^{2} = 7.
 Square Root of 7: 2.6457513110645907
 Square Root of 7 in exponential form: (7)^{½} or (7)^{0.5}
 Square Root of 7 in radical form: √7
Let's explore more about finding the square root of 7 in this minilesson.
What Is the Square Root of 7?
 The square root of a number is the number that when multiplied to itself gives the original number as the product.
 √7 = 2.645 x 2.645 or 2.645 x 2.645
Is the Square Root of 7 Rational or Irrational?
 A rational number is defined as a number 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.
 √7 = 2.645751311064591. Due to its neverending nature after the decimal point, √7 is irrational.
How to Find the Square Root of 7?
The square root of 7 can be calculated using the average method or the long division method. √7 cannot be simplified any further as it is prime. The radical form of the square root of 7 is √7.
Square Root of 7 by Average Method
 The square root of 7 will lie between the square root of the two perfect squares closer to 7.
 We will first identify the square root of 4 and the square root of 9. √4 < √7 < √9.
 Thus, we determine that the square root of 7 lies between 2 and 3. 2 < √7 < 3
 Using the average method, find 7 ÷ 3 or 7 ÷ 2.
 7 ÷ 3 = 2.33
 Find the average of this quotient obtained and 3. Average = (2.33 + 3) ÷ 2 = 5.33 ÷ 2 = 2.66
 Thus, √7 = 2.66 by the average method.
Square Root of 7 by Long Division Method
 Write 7 as 7.000000. Consider the number in pairs from the right. So 7 stands alone.
 Now divide 7 with a number such that number × number gives 7 or a number lesser than that. We determine 2 × 2 = 4
 Complete the division process. Obtain 2 as the quotient and 3 as the remainder. Bring down the first pair of zeros.
 Double the quotient obtained. Now 2 × 2 forms the new divisor in the tens place.
 Find a number which in the units place along with 40, fetches the product 300 or a number lesser than that.
 We find that 6 × 46 gives 276. Complete the division and get the remainder as 24.
 Now our quotient is 2.6. Double this and get 520 as our new divisor.
 Bring down the next pair of zeros. Find the number that with 520 gives 2400 or a number lesser than that.
 We conclude 4 × 524 = 2096. Complete the division.
 Repeat the same division process until we get the quotient approximated to 3 digits.
 Thus, we have evaluated √7 = 2.645.
Explore square roots using illustrations and interactive examples.
Important Notes
 The square root of 7 is expressed as √7 in the radical form and as 7^{½} in the exponential form.
 The square root of a number is both negative and positive for the same numerical value, i.e., the square root of 7 is +2.645 or 2.645.
Tips and Tricks
 The square root of 7 lies between the perfect squares closer to 7. Thus, √7 lies between 2 and 3.
 Use the average method to determine the approximate value of 7 and the division method to determine the accurate value of √7.
Square Root of 7 Solved Examples

Example 1: The area of the pizza that Mike bought is 22 square units. What will be the radius of the pizza?
Solution:
Area of the pizza = π r^{2} square units
π r^{2 }= 22
r^{2 }= 22 × 7 / 22
r^{2 }= 7. This implies r = √7
Thus, the radius of the pizza is 2.645 units.

Example 2 : If a^{2 }= 0.07, find a.
Solution:
Given a^{2 }= 0.07
a^{2 }= (7/100)
a = √(7/100)
= √7/√100
= √7/10
= 2.645/10
Thus, a = 0.2645

Example 3: In a rightangled triangle, the two legs measure √3 and 2 respectively. What is the measure of the hypotenuse?
Solution:
According to the Pythagorean theorem,
Hypotenuse^{2} = leg1^{2}+ leg2^{2}
Hypotenuse^{2} = ( √3)^{2 }+ 2^{2}
Taking square root, we get √Hypotenuse^{2} = √(( √3)^{2 }+ 2^{2 })
Hypotenuse = √(3+4) = √7 = 2.645
Thus, the hypotenuse measures 2.645.
FAQs on the Square Root of 7
What is the Value of the Square Root of 7?
The square root of 7 is 2.64575.
Why is the Square Root of 7 an Irrational Number?
The number 7 is prime. This implies that the number 7 is without its pair and is not in the power of 2. Therefore, the square root of 7 is irrational.
Is the number 7 a Perfect Square?
The number 7 is prime. This implies that the square root of 7 cannot be expressed as a product of two equal integers. Therefore, the number 7 is not a perfect square.
What is the Square Root of 7 in Simplest Radical Form?
The number 7 is a prime number. This implies that the number 7 is without its pair and is not in the power of 2. Therefore, the radical form of square root of 7 cannot be simplified further.
What is the Value of 20 square root 7?
The square root of 7 is 2.646. Therefore, 20 √7 = 20 × 2.646 = 52.915.
What is the Square Root of 7?
The square root of 7 is an imaginary number. It can be written as √7 = √1 × √7 = i √7 = 2.645i
where i = √1 and it is called the imaginary unit.
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