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

Square Root of 298

The square root of 298 is expressed as √298 in the radical form and as (298)^½ or (298)^0.5 in the exponent form. The square root of 298 rounded up to 5 decimal places is 17.26268. It is the positive solution of the equation x² = 298.

Square Root of 298: 17.26267650163207
Square Root of 298 in exponential form: (298)^½ or (298)^0.5
Square Root of 298 in radical form: √298

Square Root of 298

1.	What is the Square Root of 298?
2.	How to find the Square Root of 298?
3.	Is the Square Root of 298 Irrational?
4.	FAQs

What is the Square Root of 298?

The square root of 298, (or root 298), is the number which when multiplied by itself gives the product as 298. Therefore, the square root of 298 = √298 = 17.26267650163207.

☛ Check: Square Root Calculator

How to Find Square Root of 298?

Square Root of 298 by Long Division Method

Value of √298 by Long Division Method

Explanation:

Forming pairs: 02 and 98
Find a number Y (1) such that whose square is <= 2. Now divide 02 by 1 with quotient as 1.
Bring down the next pair 98, to the right of the remainder 1. The new dividend is now 198.
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 7) such that 2Z × Z <= 198. After finding Z, together 2 and Z (7) form a new divisor 27 for the new dividend 198.
Divide 198 by 27 with the quotient as 7, giving the remainder = 198 - 27 × 7 = 198 - 189 = 9.
Now, let's find the decimal places after the quotient 17.
Bring down 00 to the right of this remainder 9. The new dividend is now 900.
Add the last digit of quotient to divisor i.e. 7 + 27 = 34. To the right of 34, find a digit Z (which is 2) such that 34Z × Z <= 900. Together they form a new divisor (342) for the new dividend (900).
Divide 900 by 342 with the quotient as 2, giving the remainder = 900 - 342 × 2 = 900 - 684 = 216.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 298.

Therefore, the square root of 298 by long division method is 17.2 approximately.

Is Square Root of 298 Irrational?

The actual value of √298 is undetermined. The value of √298 up to 25 decimal places is 17.26267650163206875820607. Hence, the square root of 298 is an irrational number.

☛ Also Check:

Square Root of 92 - √92 = 9.59166
Square Root of 900 - √900 = 30
Square Root of 192 - √192 = 13.85641
Square Root of 162 - √162 = 12.72792
Square Root of 10 - √10 = 3.16228
Square Root of 512 - √512 = 22.62742
Square Root of 45 - √45 = 6.70820

Square Root of 298 Solved Examples

Example 1: Solve the equation x² − 298 = 0

Solution:

x² - 298 = 0 i.e. x² = 298
x = ±√298
Since the value of the square root of 298 is 17.263,
⇒ x = +√298 or -√298 = 17.263 or -17.263.
Example 2: If the surface area of a cube is 1788 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 = 1788 in²
⇒ a = ±√298 in
Since length can't be negative,
⇒ a = √298
We know that the square root of 298 is 17.263.
⇒ a = 17.263 in
Example 3: If the area of an equilateral triangle is 298√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 = 298√3 in²
⇒ a = ±√1192 in
Since length can't be negative,
⇒ a = √1192 = 2 √298
We know that the square root of 298 is 17.263.
⇒ a = 34.525 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 298

What is the Value of the Square Root of 298?

The square root of 298 is 17.26267.

Why is the Square Root of 298 an Irrational Number?

Upon prime factorizing 298 i.e. 2¹ × 149¹, 2 is in odd power. Therefore, the square root of 298 is irrational.

Is the number 298 a Perfect Square?

The prime factorization of 298 = 2¹ × 149¹. Here, the prime factor 2 is not in the pair. Therefore, 298 is not a perfect square.

What is the Square of the Square Root of 298?

The square of the square root of 298 is the number 298 itself i.e. (√298)² = (298)^2/2 = 298.

What is the Value of 15 square root 298?

The square root of 298 is 17.263. Therefore, 15 √298 = 15 × 17.263 = 258.940.

Evaluate 2 plus 12 square root 298

The given expression is 2 + 12 √298. We know that the square root of 298 is 17.263. Therefore, 2 + 12 √298 = 2 + 12 × 17.263 = 2 + 207.152 = 209.152

Math worksheets and
visual curriculum