find the square of 95
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Step-by-step explanation:
Square Root of 95
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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: 952 = 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 95½
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 non-terminating 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
95= 9025.