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Square Root of 596

The square root of 596 is expressed as √596 in the radical form and as (596)^½ or (596)^0.5 in the exponent form. The square root of 596 rounded up to 10 decimal places is 24.4131112315. It is the positive solution of the equation x² = 596. We can express the square root of 596 in its lowest radical form as 2 √149.

Square Root of 596: 24.413111231467404
Square Root of 596 in exponential form: (596)^½ or (596)^0.5
Square Root of 596 in radical form: √596 or 2 √149

Square Root of 596

1.	What is the Square Root of 596?
2.	How to find the Square Root of 596?
3.	Is the Square Root of 596 Irrational?
4.	FAQs

What is the Square Root of 596?

The square root of 596, (or root 596), is the number which when multiplied by itself gives the product as 596. Therefore, the square root of 596 = √596 = 2 √149 = 24.413111231467404.

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How to Find Square Root of 596?

Square Root of 596 by Long Division Method

Value of √596 by Long Division Method

Explanation:

Forming pairs: 05 and 96
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 96, to the right of the remainder 1. The new dividend is now 196.
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 <= 196. After finding Z, together 4 and Z (4) form a new divisor 44 for the new dividend 196.
Divide 196 by 44 with the quotient as 4, giving the remainder = 196 - 44 × 4 = 196 - 176 = 20.
Now, let's find the decimal places after the quotient 24.
Bring down 00 to the right of this remainder 20. The new dividend is now 2000.
Add the last digit of quotient to divisor i.e. 4 + 44 = 48. To the right of 48, find a digit Z (which is 4) such that 48Z × Z <= 2000. Together they form a new divisor (484) for the new dividend (2000).
Divide 2000 by 484 with the quotient as 4, giving the remainder = 2000 - 484 × 4 = 2000 - 1936 = 64.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 596.

Therefore, the square root of 596 by long division method is 24.4 approximately.

Is Square Root of 596 Irrational?

The actual value of √596 is undetermined. The value of √596 up to 25 decimal places is 24.41311123146740590379571. Hence, the square root of 596 is an irrational number.

☛ Also Check:

Square Root of 45 - √45 = 6.70820
Square Root of 1681 - √1681 = 41
Square Root of 51 - √51 = 7.14143
Square Root of 10 - √10 = 3.16228
Square Root of 625 - √625 = 25
Square Root of 784 - √784 = 28
Square Root of 23 - √23 = 4.79583

Square Root of 596 Solved Examples

Example 1: Solve the equation x² − 596 = 0

Solution:

x² - 596 = 0 i.e. x² = 596
x = ±√596
Since the value of the square root of 596 is 24.413,
⇒ x = +√596 or -√596 = 24.413 or -24.413.
Example 2: If the surface area of a sphere is 2384π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 2384π in²
⇒ r = ±√596 in
Since radius can't be negative,
⇒ r = √596
The square root of 596 is 24.413.
⇒ r = 24.413 in
Example 3: If the area of an equilateral triangle is 596√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 = 596√3 in²
⇒ a = ±√2384 in
Since length can't be negative,
⇒ a = √2384 = 2 √596
We know that the square root of 596 is 24.413.
⇒ a = 48.826 in

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FAQs on the Square Root of 596

What is the Value of the Square Root of 596?

The square root of 596 is 24.41311.

Why is the Square Root of 596 an Irrational Number?

Upon prime factorizing 596 i.e. 2² × 149¹, 149 is in odd power. Therefore, the square root of 596 is irrational.

What is the Square Root of 596 in Simplest Radical Form?

We need to express 596 as the product of its prime factors i.e. 596 = 2 × 2 × 149. Therefore, √596 = √2 × 2 × 149 = 2 √149. Thus, the square root of 596 in the lowest radical form is 2 √149.

Is the number 596 a Perfect Square?

The prime factorization of 596 = 2² × 149¹. Here, the prime factor 149 is not in the pair. Therefore, 596 is not a perfect square.

If the Square Root of 596 is 24.413. Find the Value of the Square Root of 5.96.

Let us represent √5.96 in p/q form i.e. √(596/100) = 5.96/10 = 2.441. Hence, the value of √5.96 = 2.441

Evaluate 7 plus 16 square root 596

The given expression is 7 + 16 √596. We know that the square root of 596 is 24.413. Therefore, 7 + 16 √596 = 7 + 16 × 24.413 = 7 + 390.610 = 397.610

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