Square Root of 95
95 is the product of 2 prime numbers 5 and 19. Thus, 95 is a semiprime number. In this mini lesson, we will learn about the square root of 95, find out whether the square root of 95 is rational or irrational, and learn to find the square root of 95 using the long division method.
 Square Root of 95 = 9.746
 Square of 95: 95^{2} = 9025
What Is the Square Root of 95?
Finding the square root of a number is to find a number which, when multiplied by itself, equals the number. In other words, it is similar to the inverse of squaring.
 (95 = 9.746 × 9.746) and (95 = 9.746 × 9.746)
 √95 = ± 9.746
 The radical form of the square root of 95 is √95
 The exponential form of the square root of 95 is 95^{½}
Is Square Root of 95 Rational or Irrational?
√95 = 9.746794344808964 and therefore, we cannot write this as a rational number of the form p/q. This is a nonterminating decimal. Thus, the square root of 95 is irrational.
How to Find the Square Root of 95?
The square root of 95 or any number can be calculated in many ways. Two of them are the approximation method and the long division method.
Square Root of 95 by Approximation Method
 Take two perfect square numbers which are just smaller than 95 and just greater than 95. √81 < √95 < √100
 9 < √95 < 10
 Using the average method, divide 95 by 9 or 10.
 Let us divide by 10⇒ 95 ÷ 10 = 9.5
 Find the average of 9.5 and 10
 (9.5 + 10) / 2 = 19.5 ÷ 2 = 9.75
 √95 ≈ 9.75
Square Root of 95 by the Long Division Method
The long division method helps us find a more accurate value of the square root of any number. Let's see how to find the square root of 95 using the long division method.
 Write 95 as 95.00 00 00
 Find a number × number that gives the product 95 or less than that.
 We know that 9 × 9 = 81. Subtract this from 95 and we get the remainder as 14. Bring down the pair of zeros. 1400 is our new dividend.
 Double the quotient. We obtain 18. To find the new divisor, 18n × n should be less than or equal to 1400.
 We determine that 187 × 7 = 1309. Subtract this from 1400 and obtain the remainder as 91. Bring down the next pair of zeros. 9100 is the new dividend.
 Double the quotient 9.7⇒ 194 and let us have 194n × n as our new divisor.
 We determine 1944 × 4 = 7776 as our product. Subtract this from 9100. We obtain 1324 as the remainder. Bring down the next pair of zeros.
 Repeat the process until we obtain the quotient approximated to 3 decimal places.
 √95 = ± 9.746
Tips and Tricks
√95 lies between the two perfect squares √81 and √100 and clearly, lies between 9 and 10. Thus, it is not a whole number and it is irrational. Use the average method to mentally evaluate the approximate value of √95.
Explore square roots using illustrations and interactive examples:
Important Notes
 The square root of 95 is ± 9.746 and it is 95 raised to the power half.
 √95 is not a perfect square. √95 lies between the two perfect square √81 and √100.
 √95 is an irrational number.
Square Root of 95 Solved Examples

Example 1: Charles found that onefifth of the square of a number is 19. Help him find the number.
Solution:
(1/5) n^{2 }= 19
n^{2 }= 95
n = √95 = 9.746The number Charles is looking for is 9.746

Example 2: Evaluate: (√95 × √95) / √9025
Solution:
(√95 × √95) = 95
√9025 = 95
(√95 × √95) / √9025 = 95 ÷ 95 = 1(√95 × √95) / √9025 = 1
FAQs on Square Root of 95
What is the square root of 95?
The square root of 95 is 9.746
What is the square root of 95 simplified?
√95 cannot be simplified to its radical form.
Is the square root of 95 real or imaginary?
The square root of 95 is real.
Is square root of 95 a rational number?
√95 is an irrational number because the value of √95 is a nonterminating decimal.
How to find the square root of 95 to the nearest hundredth?
The square root of 95 is evaluated using the division method and rounded off to the nearest hundredth. √95 = 9.746. We round it off to the nearest hundredth as 9.75