The square root of 99 is expressed as √99 in the radical kind and as (99)½ or (99)0.5 in the exponent form. The square source of 99 rounded as much as 7 decimal areas is 9.9498744. The is the positive solution the the equation x2 = 99. We can express the square source of 99 in its lowest radical kind as 3 √11.

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Square root of 99: 9.9498743710662Square root of 99 in exponential form: (99)½ or (99)0.5Square source of 99 in radical form: √99 or 3 √11
 1 What Is the Square source of 99? 2 Is Square source of 99 reasonable or Irrational? 3 How to uncover the Square root of 99? 4 Important note on Square root of 99 5 Challenging Questions 6 FAQs ~ above Square root of 99

The square source of 99 is written in the radical form as √99. This shows 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 = 99Thus, √99 = ± 9.949In the exponential form, us denote √99 together (99)½

√99 cannot be created in the kind of p/q. Hence, it is an irrational number. The square root of 99 is one irrational number together the number after the decimal suggest go approximately infinity. √99 = 9.9498743710662.

The square source of 99 or any type of number deserve to be calculation in many ways. Two vital methods are the prime factorization method and the long division method.

Square source of 99 in the most basic Radical Form

99 = 3 × 3 × 11Taking square source on both the sides, us get√99 = √(3 × 3 × 11)99½ = ( 3 × 3 × 11)½99½ = ( 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 department Method

The long division method helps us to uncover a much more accurate worth of the square root of any kind of number. Let"s see how to discover the square root of 99 by the long department 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 discover a quotient i m sorry is the same as the divisor. Main point the quotient and also the divisor. 9 × 9 = 81 and subtract the result from 99. Us will acquire the remainder as 18. Step 3: Now dual the quotient obtained in action 2. Here, that is 2 × 9 = 18. 180 i do not care the brand-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 must choose a number such that once it is included to 180 and this sum is multiplied with the same number, we gain a number less than 1800. 180+ 9 =189 and 189 × 9 = 1701. Subtract 1701 from 1800. We get 99 as the remainder. Bring under the following pair of zeros so that it i do not care 9900. This is the brand-new dividend.Step 6: Now dual the quotient. Here it is 198. 1980 is the new divisor. Now discover a number because that the unit"s ar that when multiplied to the divisor gives 9900 or less. We uncover that 1984 × 4 = 7936. Discover the remainder.Step 7: Repeat the process until we acquire the square source of 99 approximated to two places. Thus, √99 = 9.949

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Important Notes

The square root of 99 is 99½ in the exponential kind and 3√11 in its simplest radical form.√99 = 9.94999 is closer come 100 and hence, the square root of 99 have the right to be approximated to 10.

Challenging Questions

What is the least number that can be multiply to 99 to make it a perfect square? What is the square root of that perfect square?Find the sum of the an initial 10 continually odd numbers. Subtract 1 from it. What pattern do you observe?

Example 1: given x2 = y, then find x if y = 0.99

Solution:

x2 = y ⇒ √y = x

x2 = 0.99

x = √0.99

√0.99 = √(99/100)

=√99 ÷ √100

= 9.949 ÷ 10 = 0.9949

Thus, x = 0.9949

Example 2: An military officer arranges his soldiers in together a way that there are equal variety of rows and also columns. How plenty of soldiers will be left out from this setup if over there are 99 soldiers to it is in arranged? How countless will have to be included to do the preferred arrangement?

Solution:

Number that rows multiply by the number that columns should equal the total variety of soldiers.

Let united state assume, the variety of rows = the number of columns = a

a × a = 99 ⇒ a2 = 99

a = 9.9949. We cannot have a decimal number. Therefore, we need to look because that the totality numbers.

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The nearest perfect square less than 99 is 81. A = 9 × 9 = 81

99 - 81 = 18

The nearest perfect square better than 99 is 100. 10 × 10 = 100

100 - 99 = 1

If the 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 requirements one an ext soldier.