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Square Root of 588

The square root of 588 is expressed as √588 in the radical form and as (588)^½ or (588)^0.5 in the exponent form. The square root of 588 rounded up to 7 decimal places is 24.2487113. It is the positive solution of the equation x² = 588. We can express the square root of 588 in its lowest radical form as 14 √3.

Square Root of 588: 24.24871130596428
Square Root of 588 in exponential form: (588)^½ or (588)^0.5
Square Root of 588 in radical form: √588 or 14 √3

Square Root of 588

1.	What is the Square Root of 588?
2.	How to find the Square Root of 588?
3.	Is the Square Root of 588 Irrational?
4.	FAQs

What is the Square Root of 588?

The square root of 588, (or root 588), is the number which when multiplied by itself gives the product as 588. Therefore, the square root of 588 = √588 = 14 √3 = 24.24871130596428.

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How to Find Square Root of 588?

Square Root of 588 by Long Division Method

Value of √588 by Long Division Method

Explanation:

Forming pairs: 05 and 88
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 88, to the right of the remainder 1. The new dividend is now 188.
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 <= 188. After finding Z, together 4 and Z (4) form a new divisor 44 for the new dividend 188.
Divide 188 by 44 with the quotient as 4, giving the remainder = 188 - 44 × 4 = 188 - 176 = 12.
Now, let's find the decimal places after the quotient 24.
Bring down 00 to the right of this remainder 12. The new dividend is now 1200.
Add the last digit of quotient to divisor i.e. 4 + 44 = 48. To the right of 48, find a digit Z (which is 2) such that 48Z × Z <= 1200. Together they form a new divisor (482) for the new dividend (1200).
Divide 1200 by 482 with the quotient as 2, giving the remainder = 1200 - 482 × 2 = 1200 - 964 = 236.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 588.

Therefore, the square root of 588 by long division method is 24.2 approximately.

Is Square Root of 588 Irrational?

The actual value of √588 is undetermined. The value of √588 up to 25 decimal places is 24.24871130596428210938425. Hence, the square root of 588 is an irrational number.

☛ Also Check:

Square Root of 120 - √120 = 10.95445
Square Root of 109 - √109 = 10.44031
Square Root of 49 - √49 = 7
Square Root of 41 - √41 = 6.40312
Square Root of 56 - √56 = 7.48331
Square Root of 106 - √106 = 10.29563
Square Root of 80 - √80 = 8.94427

Square Root of 588 Solved Examples

Example 1: Solve the equation x² − 588 = 0

Solution:

x² - 588 = 0 i.e. x² = 588
x = ±√588
Since the value of the square root of 588 is 24.249,
⇒ x = +√588 or -√588 = 24.249 or -24.249.
Example 2: If the area of an equilateral triangle is 588√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 = 588√3 in²
⇒ a = ±√2352 in
Since length can't be negative,
⇒ a = √2352 = 2 √588
We know that the square root of 588 is 24.249.
⇒ a = 48.497 in
Example 3: If the surface area of a cube is 3528 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 = 3528 in²
⇒ a = ±√588 in
Since length can't be negative,
⇒ a = √588
We know that the square root of 588 is 24.249.
⇒ a = 24.249 in

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FAQs on the Square Root of 588

What is the Value of the Square Root of 588?

The square root of 588 is 24.24871.

Why is the Square Root of 588 an Irrational Number?

Upon prime factorizing 588 i.e. 2² × 3¹ × 7², 3 is in odd power. Therefore, the square root of 588 is irrational.

Is the number 588 a Perfect Square?

The prime factorization of 588 = 2² × 3¹ × 7². Here, the prime factor 3 is not in the pair. Therefore, 588 is not a perfect square.

What is the Square Root of -588?

The square root of -588 is an imaginary number. It can be written as √-588 = √-1 × √588 = i √588 = 24.248i
where i = √-1 and it is called the imaginary unit.

If the Square Root of 588 is 24.249. Find the Value of the Square Root of 5.88.

Let us represent √5.88 in p/q form i.e. √(588/100) = 5.88/10 = 2.425. Hence, the value of √5.88 = 2.425

What is the Square Root of 588 in Simplest Radical Form?

We need to express 588 as the product of its prime factors i.e. 588 = 2 × 2 × 3 × 7 × 7. Therefore, √588 = √2 × 2 × 3 × 7 × 7 = 14 √3. Thus, the square root of 588 in the lowest radical form is 14 √3.

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