98 is an also composite number. The square the 98 deserve to be created as (100-2)2 = (100)2 + (2)2 - (2 × 100 × 2) = 10000 + 4 - 400 = 9604.

You are watching: Square root of 98 in simplest radical form

In this mini-lesson, let united state learn how to find the square root of 98.

Square root of 98: 9.89949493661Square of 98: 9604
1.What Is the Square source of 98?
2.Is the Square root of 98 rational or Irrational?
3.How to uncover the Square source of 98?
4.Thinking out of the Box!
5.FAQs ~ above Square source of 98
6.Important note on Square source of 98

What Is the Square root of 98?

The square root of 98 is a number whose square gives the original number. What number can that be? through trial and also error method, we have the right to observe that there is no integer who square is 98. Yet we can discover the square root of 98 making use of a calculator. 

√98 = 9.899494To inspect this answer, uncover (9.899494)2 and we have the right to see that we gain a number 97.9999815... I beg your pardon is very close to 98.

Is the Square root of 98 reasonable or Irrational?

A rational number is a number i beg your pardon is: 

either terminatingor non-terminating and also has a repeating pattern in that decimal part.

√98 = 9.899494, clearly, this is non-terminating and also the decimal component has no repeating pattern. Thus, it is not a reasonable number. √98 is an irrational number.


We can find the square root of 98 using assorted methods.

Repeated subtraction Prime factorizationEstimation and also approximationLong division

Square root of 98 by prime Factorization

The element factorization of 98 is 2 × 7 × 7. We can see the 7 is the only pair of the very same numbers. Thus, 98 cannot be simplified any kind of further and hence, √98 is 7√2.

Square source of 98 through Long department Method

The value of the square source of 98 by the long department method is composed of the following steps:

Step 1: starting from the right, we will certainly pair up the number by putting a bar above them.

Step 2: Find a number together that as soon as you main point it with itself, the product is less than or equal to 98. So, the number is 9. Keeping the divisor together 9, we gain the quotient together 9 and the remainder 98 - 81 = 17.

Step 3: double the divisor and also enter it through a blank on its right. Guess: v the largest possible digit to to fill the empty which will also become the new digit in the quotient, together that when the new divisor is multiply to the new quotient, the product is less than or equal to the dividend. Divide and also write the remainder.

See more: How To Make A Wizard In Little Alchemy, How To Make Wizard In Little Alchemy

Repeat this process to get the decimal areas you want. Hence √98 = 9.89

*

Explore square roots using illustrations and also interactive examples.


Think Tank


Can the value of a square source be an unfavorable as well? Hint: What is the square that a negative number?Is √-98 a real number?Hint: Is there any kind of real number whose square is negative?
Important Notes
98 lies in between 81 and 100. So, √98 lies in between √81 and also √100, i.e. √98 lies between 9 and 10.The prime factorization technique is provided to compose the square root of a non-perfect square number in the simplest radical form. Because that example, 45 = 3 × 3 × 5= 32 × 5 and also so, √45 = √32 × √5 = 3 √5