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Square Root of 578

The square root of 578 is expressed as √578 in the radical form and as (578)^½ or (578)^0.5 in the exponent form. The square root of 578 rounded up to 8 decimal places is 24.04163056. It is the positive solution of the equation x² = 578. We can express the square root of 578 in its lowest radical form as 17 √2.

Square Root of 578: 24.041630560342615
Square Root of 578 in exponential form: (578)^½ or (578)^0.5
Square Root of 578 in radical form: √578 or 17 √2

Square Root of 578

1.	What is the Square Root of 578?
2.	How to find the Square Root of 578?
3.	Is the Square Root of 578 Irrational?
4.	FAQs

What is the Square Root of 578?

The square root of 578, (or root 578), is the number which when multiplied by itself gives the product as 578. Therefore, the square root of 578 = √578 = 17 √2 = 24.041630560342615.

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How to Find Square Root of 578?

Square Root of 578 by Long Division Method

Value of √578 by Long Division Method

Explanation:

Forming pairs: 05 and 78
Find a number Y (2) such that whose square is <= 5. Now divide 05 by 2 with quotient as 2.
Bring down the next pair 78, to the right of the remainder 1. The new dividend is now 178.
Add the last digit of the quotient (2) to the divisor (2) i.e. 2 + 2 = 4. To the right of 4, find a digit Z (which is 4) such that 4Z × Z <= 178. After finding Z, together 4 and Z (4) form a new divisor 44 for the new dividend 178.
Divide 178 by 44 with the quotient as 4, giving the remainder = 178 - 44 × 4 = 178 - 176 = 2.
Now, let's find the decimal places after the quotient 24.
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 + 44 = 48. To the right of 48, find a digit Z (which is 0) such that 48Z × Z <= 200. Together they form a new divisor (480) for the new dividend (200).
Divide 200 by 480 with the quotient as 0, giving the remainder = 200 - 480 × 0 = 200 - 0 = 200.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 578.

Therefore, the square root of 578 by long division method is 24.0 approximately.

Is Square Root of 578 Irrational?

The actual value of √578 is undetermined. The value of √578 up to 25 decimal places is 24.04163056034261582962871. Hence, the square root of 578 is an irrational number.

☛ Also Check:

Square Root of 52 - √52 = 7.21110
Square Root of 106 - √106 = 10.29563
Square Root of 250 - √250 = 15.81139
Square Root of 1521 - √1521 = 39
Square Root of 8 - √8 = 2.82843
Square Root of 85 - √85 = 9.21954
Square Root of 48 - √48 = 6.92820

Square Root of 578 Solved Examples

Example 1: Solve the equation x² − 578 = 0

Solution:

x² - 578 = 0 i.e. x² = 578
x = ±√578
Since the value of the square root of 578 is 24.042,
⇒ x = +√578 or -√578 = 24.042 or -24.042.
Example 2: If the surface area of a cube is 3468 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 = 3468 in²
⇒ a = ±√578 in
Since length can't be negative,
⇒ a = √578
We know that the square root of 578 is 24.042.
⇒ a = 24.042 in
Example 3: If the area of a circle is 578π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 578π in²
⇒ r = ±√578 in
Since radius can't be negative,
⇒ r = √578
The square root of 578 is 24.042.
⇒ r = 24.042 in

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FAQs on the Square Root of 578

What is the Value of the Square Root of 578?

The square root of 578 is 24.04163.

Why is the Square Root of 578 an Irrational Number?

Upon prime factorizing 578 i.e. 2¹ × 17², 2 is in odd power. Therefore, the square root of 578 is irrational.

Is the number 578 a Perfect Square?

The prime factorization of 578 = 2¹ × 17². Here, the prime factor 2 is not in the pair. Therefore, 578 is not a perfect square.

Evaluate 12 plus 8 square root 578

The given expression is 12 + 8 √578. We know that the square root of 578 is 24.042. Therefore, 12 + 8 √578 = 12 + 8 × 24.042 = 12 + 192.333 = 204.333

What is the Square Root of -578?

The square root of -578 is an imaginary number. It can be written as √-578 = √-1 × √578 = i √578 = 24.041i
where i = √-1 and it is called the imaginary unit.

If the Square Root of 578 is 24.042. Find the Value of the Square Root of 5.78.

Let us represent √5.78 in p/q form i.e. √(578/100) = 5.78/10 = 2.404. Hence, the value of √5.78 = 2.404

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