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

Square Root of 294

The square root of 294 is expressed as √294 in the radical form and as (294)^½ or (294)^0.5 in the exponent form. The square root of 294 rounded up to 6 decimal places is 17.146428. It is the positive solution of the equation x² = 294. We can express the square root of 294 in its lowest radical form as 7 √6.

Square Root of 294: 17.146428199482248
Square Root of 294 in exponential form: (294)^½ or (294)^0.5
Square Root of 294 in radical form: √294 or 7 √6

Square Root of 294

1.	What is the Square Root of 294?
2.	How to find the Square Root of 294?
3.	Is the Square Root of 294 Irrational?
4.	FAQs

What is the Square Root of 294?

The square root of 294, (or root 294), is the number which when multiplied by itself gives the product as 294. Therefore, the square root of 294 = √294 = 7 √6 = 17.146428199482248.

☛ Check: Square Root Calculator

How to Find Square Root of 294?

Square Root of 294 by Long Division Method

Value of √294 by Long Division Method

Explanation:

Forming pairs: 02 and 94
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 94, to the right of the remainder 1. The new dividend is now 194.
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 <= 194. After finding Z, together 2 and Z (7) form a new divisor 27 for the new dividend 194.
Divide 194 by 27 with the quotient as 7, giving the remainder = 194 - 27 × 7 = 194 - 189 = 5.
Now, let's find the decimal places after the quotient 17.
Bring down 00 to the right of this remainder 5. The new dividend is now 500.
Add the last digit of quotient to divisor i.e. 7 + 27 = 34. To the right of 34, find a digit Z (which is 1) such that 34Z × Z <= 500. Together they form a new divisor (341) for the new dividend (500).
Divide 500 by 341 with the quotient as 1, giving the remainder = 500 - 341 × 1 = 500 - 341 = 159.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 294.

Therefore, the square root of 294 by long division method is 17.1 approximately.

Is Square Root of 294 Irrational?

The actual value of √294 is undetermined. The value of √294 up to 25 decimal places is 17.14642819948224668738099. Hence, the square root of 294 is an irrational number.

☛ Also Check:

Square Root of 400 - √400 = 20
Square Root of 136 - √136 = 11.66190
Square Root of 85 - √85 = 9.21954
Square Root of 28 - √28 = 5.29150
Square Root of 2 - √2 = 1.41421
Square Root of 240 - √240 = 15.49193
Square Root of 92 - √92 = 9.59166

Square Root of 294 Solved Examples

Example 1: Solve the equation x² − 294 = 0

Solution:

x² - 294 = 0 i.e. x² = 294
x = ±√294
Since the value of the square root of 294 is 17.146,
⇒ x = +√294 or -√294 = 17.146 or -17.146.
Example 2: If the surface area of a sphere is 1176π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 1176π in²
⇒ r = ±√294 in
Since radius can't be negative,
⇒ r = √294
The square root of 294 is 17.146.
⇒ r = 17.146 in
Example 3: If the surface area of a cube is 1764 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 = 1764 in²
⇒ a = ±√294 in
Since length can't be negative,
⇒ a = √294
We know that the square root of 294 is 17.146.
⇒ a = 17.146 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 294

What is the Value of the Square Root of 294?

The square root of 294 is 17.14642.

Why is the Square Root of 294 an Irrational Number?

Upon prime factorizing 294 i.e. 2¹ × 3¹ × 7², 2 is in odd power. Therefore, the square root of 294 is irrational.

What is the Square Root of -294?

The square root of -294 is an imaginary number. It can be written as √-294 = √-1 × √294 = i √294 = 17.146i
where i = √-1 and it is called the imaginary unit.

If the Square Root of 294 is 17.146. Find the Value of the Square Root of 2.94.

Let us represent √2.94 in p/q form i.e. √(294/100) = 2.94/10 = 1.715. Hence, the value of √2.94 = 1.715

What is the Value of 17 square root 294?

The square root of 294 is 17.146. Therefore, 17 √294 = 17 × 17.146 = 291.489.

Evaluate 14 plus 10 square root 294

The given expression is 14 + 10 √294. We know that the square root of 294 is 17.146. Therefore, 14 + 10 √294 = 14 + 10 × 17.146 = 14 + 171.464 = 185.464

Math worksheets and
visual curriculum