98 is an even composite number. The square of 98 have the right to be written as (100-2)2 = (100)2 + (2)2 - (2 × 100 × 2) = 10000 + 4 - 400 = 9604.

You are watching: What is the square root of 98 in radical form

In this mini-leskid, let us learn exactly how to discover the square root of 98.

Square Root of 98: 9.89949493661Square of 98: 9604
1.What Is the Square Root of 98?
2.Is the Square Root of 98 Rational or Irrational?
3.How to Find the Square Root of 98?
4.Thinking Out of the Box!
5.FAQs on Square Root of 98
6.Important Notes on Square Root 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 could that be? By trial and error technique, we deserve to observe that tright here is no integer whose square is 98. But we have the right to uncover the square root of 98 using a calculator. 

√98 = 9.899494To inspect this answer, find (9.899494)2 and also we have the right to watch that we acquire a number 97.9999815... which is incredibly cshed to 98.

Is the Square Root of 98 Rational or Irrational?

A rational number is a number which is: 

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

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

We can find the square root of 98 making use of assorted approaches.

Repeated subtraction Prime factorizationEstimation and also approximationLong division

Square Root of 98 by Prime Factorization

The prime factorization of 98 is 2 × 7 × 7. We can watch that 7 is the only pair of the very same numbers. Hence, 98 cannot be streamlined any further and therefore, √98 is 7√2.

Square Root of 98 by Long Division Method

The value of the square root of 98 by the lengthy department technique consists of the following steps:

Step 1: Starting from the right, we will certainly pair up the digits by placing a bar over them.

Tip 2: Find a number such that as soon as you multiply it with itself, the product is much less than or equal to 98. So, the number is 9. Keeping the divisor as 9, we acquire the quotient as 9 and the remainder 98 - 81 = 17.

Tip 3: Double the divisor and also enter it with a empty on its ideal. Guess the largest possible digit to fill the empty which will additionally end up being the new digit in the quotient, such that once the brand-new divisor is multiplied to the brand-new quotient, the product is much less than or equal to the dividend. Divide and write the remainder.

See more: Advantages And Disadvantages Of Technology In Agriculture, What Are The

Repeat this process to obtain the decimal areas you want. Thus √98 = 9.89


Explore square roots utilizing illustrations and also interenergetic examples.

Think Tank

Can the worth of a square root be negative as well? Hint: What is the square of an adverse number?Is √-98 a genuine number?Hint: Is tbelow any type of actual number whose square is negative?
Important Notes
98 lies in between 81 and also 100. So, √98 lies in between √81 and also √100, i.e. √98 lies between 9 and 10.The prime factorization technique is offered to create the square root of a non-perfect square number in the simplest radical create. For example, 45 = 3 × 3 × 5= 32 × 5 and also so, √45 = √32 × √5 = 3 √5