A day full of math games & activities. Find one near you.

Square Root of 198

The square root of 198 is expressed as √198 in the radical form and as (198)^½ or (198)^0.5 in the exponent form. The square root of 198 rounded up to 9 decimal places is 14.071247279. It is the positive solution of the equation x² = 198. We can express the square root of 198 in its lowest radical form as 3 √22.

Square Root of 198: 14.071247279470288
Square Root of 198 in exponential form: (198)^½ or (198)^0.5
Square Root of 198 in radical form: √198 or 3 √22

Square Root of 198

1.	What is the Square Root of 198?
2.	How to find the Square Root of 198?
3.	Is the Square Root of 198 Irrational?
4.	FAQs

What is the Square Root of 198?

The square root of 198, (or root 198), is the number which when multiplied by itself gives the product as 198. Therefore, the square root of 198 = √198 = 3 √22 = 14.071247279470288.

☛ Check: Square Root Calculator

How to Find Square Root of 198?

Square Root of 198 by Long Division Method

Value of √198 by Long Division Method

Explanation:

Forming pairs: 01 and 98
Find a number Y (1) such that whose square is <= 1. Now divide 01 by 1 with quotient as 1.
Bring down the next pair 98, to the right of the remainder 0. The new dividend is now 98.
Add the last digit of the quotient (1) to the divisor (1) i.e. 1 + 1 = 2. To the right of 2, find a digit Z (which is 4) such that 2Z × Z <= 98. After finding Z, together 2 and Z (4) form a new divisor 24 for the new dividend 98.
Divide 98 by 24 with the quotient as 4, giving the remainder = 98 - 24 × 4 = 98 - 96 = 2.
Now, let's find the decimal places after the quotient 14.
Bring down 00 to the right of this remainder 2. The new dividend is now 200.
Add the last digit of quotient to divisor i.e. 4 + 24 = 28. To the right of 28, find a digit Z (which is 0) such that 28Z × Z <= 200. Together they form a new divisor (280) for the new dividend (200).
Divide 200 by 280 with the quotient as 0, giving the remainder = 200 - 280 × 0 = 200 - 0 = 200.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 198.

Therefore, the square root of 198 by long division method is 14.0 approximately.

Is Square Root of 198 Irrational?

The actual value of √198 is undetermined. The value of √198 up to 25 decimal places is 14.07124727947028866369689. Hence, the square root of 198 is an irrational number.

☛ Also Check:

Square Root of 1296 - √1296 = 36
Square Root of 400 - √400 = 20
Square Root of 99 - √99 = 9.94987
Square Root of 49 - √49 = 7
Square Root of 11 - √11 = 3.31662
Square Root of 325 - √325 = 18.02776
Square Root of 40 - √40 = 6.32456

Square Root of 198 Solved Examples

Example 1: Solve the equation x² − 198 = 0

Solution:

x² - 198 = 0 i.e. x² = 198
x = ±√198
Since the value of the square root of 198 is 14.071,
⇒ x = +√198 or -√198 = 14.071 or -14.071.
Example 2: If the area of an equilateral triangle is 198√3 in². Find the length of one of the sides of the triangle.

Solution:

Let 'a' be the length of one of the sides of the equilateral triangle.
⇒ Area of the equilateral triangle = (√3/4)a² = 198√3 in²
⇒ a = ±√792 in
Since length can't be negative,
⇒ a = √792 = 2 √198
We know that the square root of 198 is 14.071.
⇒ a = 28.142 in
Example 3: If the surface area of a cube is 1188 in². Find the length of the side of the cube.

Solution:

Let 'a' be the length of the side of the cube.
⇒ Area of the cube = 6a² = 1188 in²
⇒ a = ±√198 in
Since length can't be negative,
⇒ a = √198
We know that the square root of 198 is 14.071.
⇒ a = 14.071 in

go to slide go to slide go to slide

Ready to see the world through math’s eyes?

Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything.

Book a Free Trial Class

FAQs on the Square Root of 198

What is the Value of the Square Root of 198?

The square root of 198 is 14.07124.

Why is the Square Root of 198 an Irrational Number?

Upon prime factorizing 198 i.e. 2¹ × 3² × 11¹, 2 is in odd power. Therefore, the square root of 198 is irrational.

What is the Square of the Square Root of 198?

The square of the square root of 198 is the number 198 itself i.e. (√198)² = (198)^2/2 = 198.

If the Square Root of 198 is 14.071. Find the Value of the Square Root of 1.98.

Let us represent √1.98 in p/q form i.e. √(198/100) = 1.98/10 = 1.407. Hence, the value of √1.98 = 1.407

What is the Square Root of 198 in Simplest Radical Form?

We need to express 198 as the product of its prime factors i.e. 198 = 2 × 3 × 3 × 11. Therefore, √198 = √2 × 3 × 3 × 11 = 3 √22. Thus, the square root of 198 in the lowest radical form is 3 √22.

Evaluate 13 plus 11 square root 198

The given expression is 13 + 11 √198. We know that the square root of 198 is 14.071. Therefore, 13 + 11 √198 = 13 + 11 × 14.071 = 13 + 154.784 = 167.784

Math worksheets and
visual curriculum