Square Root of 99
The square root of 99 is expressed as √99 in the radical form and as (99)^{½} or (99)^{0.5} in the exponent form. The square root of 99 rounded up to 7 decimal places is 9.9498744. It is the positive solution of the equation x^{2} = 99. We can express the square root of 99 in its lowest radical form as 3 √11.
 Square Root of 99: 9.9498743710662
 Square Root of 99 in exponential form: (99)^{½} or (99)^{0.5}
 Square Root of 99 in radical form: √99 or 3 √11
What Is the Square Root of 99?
 The square root of 99 is written in the radical form as √99.
 This indicates that there is a number a such that: a × a = 99.
 a^{2} = 99 ⇒ a = √99
 9.949 × 9.949 = 99 and 9.949 × 9.949 = 99
 Thus, √99 = ± 9.949
 In the exponential form, we denote √99 as (99)^{½}
Is Square Root of 99 Rational or Irrational?
√99 cannot be written in the form of p/q. Hence, it is an irrational number. The square root of 99 is an irrational number as the numbers after the decimal point go up to infinity. √99 = 9.9498743710662.
How to Find the Square Root of 99?
The square root of 99 or any number can be calculated in many ways. Two important methods are the prime factorization method and the long division method.
Square Root of 99 in the Simplest Radical Form
 To express the square root of 99 in the simplest radical form, we do the prime factorization of 99.
 99 = 3 × 3 × 11
 Taking square root on both the sides, we get
 √99 = √(3 × 3 × 11)
 99^{½} = ( 3 × 3 × 11)^{½}
 99^{½} = ( 3 × 3 × 11)^{½}
 √99 = (3 ^{2} × 11)^{½}
 √99 = (3 ^{2}) ^{½ }× (11)^{½}
 √99 = 3 √11
Square Root of 99 by the Long Division Method
The long division method helps us to find a more accurate value of the square root of any number. Let's see how to find the square root of 99 by the long division method.
 Step 1: Express 99 as 99.000000. Let's consider this number in pairs from the right. Let's take 99 as the dividend.
 Step 2: Now find a quotient which is the same as the divisor. Multiply the quotient and the divisor. 9 × 9 = 81 and subtract the result from 99. We will get the remainder as 18.
 Step 3: Now double the quotient obtained in step 2. Here, it is 2 × 9 = 18. 180 becomes the new divisor.
 Step 4: Apply a decimal after quotient 9 and bring down two zeros. We have 1800 as the dividend now.
 Step 5: We need to choose a number such that when it is added to 180 and this sum is multiplied with the same number, we get a number less than 1800. 180+ 9 =189 and 189 × 9 = 1701.
 Subtract 1701 from 1800. We get 99 as the remainder. Bring down the next pair of zeros so that it becomes 9900. This is the new dividend.
 Step 6: Now double the quotient. Here it is 198. 1980 is the new divisor. Now find a number for the unit's place that when multiplied to the divisor gives 9900 or less. We find that 1984 × 4 = 7936. Find the remainder.
 Step 7: Repeat the process until we get the square root of 99 approximated to two places. Thus, √99 = 9.949
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Important Notes
 The square root of 99 is 99^{½ }in the exponential form and 3√11 in its simplest radical form.
 √99 = 9.949
 99 is closer to 100 and hence, the square root of 99 can be approximated to 10.
Challenging Questions
 What is the least number that can be multiplied to 99 to make it a perfect square? What is the square root of that perfect square?
 Find the sum of the first 10 consecutive odd numbers. Subtract 1 from it. What pattern do you observe?
Square Root of 99 Solved Examples

Example 1: Given x^{2 }= y, then find x if y = 0.99
Solution:
x^{2 }= y ⇒ √y = x
x^{2 }= 0.99
x = √0.99
√0.99 = √(99/100)
=√99 ÷ √100
= 9.949 ÷ 10 = 0.9949
Thus, x = 0.9949

Example 2: An army officer arranges his soldiers in such a way that there are equal number of rows and columns. How many soldiers will be left out from this arrangement if there are 99 soldiers to be arranged? How many will have to be included to make the desired arrangement?
Solution:
Number of rows multiplied by the number of columns should equal the total number of soldiers.
Let us assume, the number of rows = the number of columns = a
a × a = 99 ⇒ a^{2 }= 99
a = 9.9949. We cannot have a decimal number. Therefore, we should look for the whole numbers.
The nearest perfect square less than 99 is 81. a = 9 × 9 = 81
99  81 = 18
The nearest perfect square greater than 99 is 100. 10 × 10 = 100
100  99 = 1
If he arranges 9 soldiers in 9 rows and 9 columns, 18 will be left out and if arranges 10 soldiers in 10 rows and 10 columns, he needs one more soldier.

Example 3: If the area of an equilateral triangle is 99√3 in^{2}. Find the length of one of the sides of the triangle.
Solution:
Let 'a' be the length of one of the sides of the equilateral triangle.
⇒ Area of the equilateral triangle = (√3/4)a^{2} = 99√3 in^{2}
⇒ a = ±√396 in
Since length can't be negative,
⇒ a = √396 = 2 √99
We know that the square root of 99 is 9.950.
⇒ a = 19.900 in
FAQs on the Square Root of 99
What is the Value of the Square Root of 99?
The square root of 99 is 9.94987.
Why is the Square Root of 99 an Irrational Number?
Upon prime factorizing 99 i.e. 3^{2} × 11^{1}, 11 is in odd power. Therefore, the square root of 99 is irrational.
If the Square Root of 99 is 9.950. Find the Value of the Square Root of 0.99.
Let us represent √0.99 in p/q form i.e. √(99/100) = 0.99/10 = 0.995. Hence, the value of √0.99 = 0.995
Evaluate 3 plus 18 square root 99
The given expression is 3 + 18 √99. We know that the square root of 99 is 9.950. Therefore, 3 + 18 √99 = 3 + 18 × 9.950 = 3 + 179.098 = 182.098
Is the number 99 a Perfect Square?
The prime factorization of 99 = 3^{2} × 11^{1}. Here, the prime factor 11 is not in the pair. Therefore, 99 is not a perfect square.
What is the Square Root of 99?
The square root of 99 is an imaginary number. It can be written as √99 = √1 × √99 = i √99 = 9.949i
where i = √1 and it is called the imaginary unit.
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