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 x² = 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

• 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. 
• a² = 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

√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.

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

Explore square roots using illustrations and interactive examples:

• Square root of 88
• Square root of 100
• Square root of 98
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• Square root of 98