Square Root of 98
98 is an even composite number. The square of 98 can be written as (100-2)2 = (100)2 + (2)2 - (2 × 100 × 2) = 10000 + 4 - 400 = 9604.
In this mini-lesson, let us learn how to find the square root of 98.
- Square Root of 98: 9.89949493661
- Square of 98: 9604
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 method, we can observe that there is no integer whose square is 98. But we can find the square root of 98 using a calculator.
- √98 = 9.899494
- To check this answer, find (9.899494)2 and we can see that we get a number 97.9999815... which is very close to 98.
Is the Square Root of 98 Rational or Irrational?
A rational number is a number which is:
- either terminating
- or non-terminating and has a repeating pattern in its decimal part.
√98 = 9.899494, clearly, this is non-terminating and the decimal part has no repeating pattern. Thus, it is not a rational number. √98 is an irrational number.
How to Find the Square Root of 98?
We can find the square root of 98 using various methods.
- Repeated subtraction
- Prime factorization
- Estimation and approximation
- Long division
Square Root of 98 by Prime Factorization
The prime factorization of 98 is 2 × 7 × 7. We can see that 7 is the only pair of the same numbers. Thus, 98 cannot be simplified any further and hence, √98 is 7√2.
Square Root of 98 by Long Division Method
The value of the square root of 98 by the long division method consists of the following steps:
Step 1: Starting from the right, we will pair up the digits by putting a bar above them.
Step 2: Find a number such that when you multiply it with itself, the product is less than or equal to 98. So, the number is 9. Keeping the divisor as 9, we get the quotient as 9 and the remainder 98 - 81 = 17.
Step 3: Double the divisor and enter it with a blank on its right. Guess the largest possible digit to fill the blank which will also become the new digit in the quotient, such that when the new divisor is multiplied to the new quotient, the product is less than or equal to the dividend. Divide and write the remainder.
Repeat this process to get the decimal places you want. Thus √98 = 9.89
Explore square roots using illustrations and interactive examples.
Think Tank
- Can the value of a square root be negative as well? Hint: What is the square of a negative number?
- Is √-98 a real number?
Hint: Is there any real number whose square is negative?
- 98 lies between 81 and 100. So, √98 lies between √81 and √100, i.e. √98 lies between 9 and 10.
- The prime factorization method is used to write the square root of a non-perfect square number in the simplest radical form. For example, 45 = 3 × 3 × 5= 32 × 5 and so, √45 = √32 × √5 = 3 √5
FAQs on Square Root of 98
Can the square root of 98 be simplified?
Yes, the square root of 98 can be simplified further as 7√2.
What is the perfect square of 98?
The perfect square of 98 is 9604.
What is the square root of 98 rounded to the nearest tenth?
To round the square root of 98 to its nearest tenth means to have one digit after the decimal point.
√98 = 9.899494. This can be rounded to its nearest tenth as 9.9
Is the square root of 98 a rational number?
The square root of 98 is a rational number only if 98 is a perfect square. But we know √98 is 7√2. Hence, √98 is an irrational number.
How to find the square root of 98?
The square root of 98 lies between √81 and √100, i.e. between 9 and 10. Its approximate value is 9.9.