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Square Root of 540

The square root of 540 is expressed as √540 in the radical form and as (540)^½ or (540)^0.5 in the exponent form. The square root of 540 rounded up to 7 decimal places is 23.2379001. It is the positive solution of the equation x² = 540. We can express the square root of 540 in its lowest radical form as 6 √15.

Square Root of 540: 23.2379000772445
Square Root of 540 in exponential form: (540)^½ or (540)^0.5
Square Root of 540 in radical form: √540 or 6 √15

Square Root of 540

1.	What is the Square Root of 540?
2.	How to find the Square Root of 540?
3.	Is the Square Root of 540 Irrational?
4.	FAQs

What is the Square Root of 540?

The square root of 540, (or root 540), is the number which when multiplied by itself gives the product as 540. Therefore, the square root of 540 = √540 = 6 √15 = 23.2379000772445.

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How to Find Square Root of 540?

Square Root of 540 by Long Division Method

Value of √540 by Long Division Method

Explanation:

Forming pairs: 05 and 40
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 40, to the right of the remainder 1. The new dividend is now 140.
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 3) such that 4Z × Z <= 140. After finding Z, together 4 and Z (3) form a new divisor 43 for the new dividend 140.
Divide 140 by 43 with the quotient as 3, giving the remainder = 140 - 43 × 3 = 140 - 129 = 11.
Now, let's find the decimal places after the quotient 23.
Bring down 00 to the right of this remainder 11. The new dividend is now 1100.
Add the last digit of quotient to divisor i.e. 3 + 43 = 46. To the right of 46, find a digit Z (which is 2) such that 46Z × Z <= 1100. Together they form a new divisor (462) for the new dividend (1100).
Divide 1100 by 462 with the quotient as 2, giving the remainder = 1100 - 462 × 2 = 1100 - 924 = 176.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 540.

Therefore, the square root of 540 by long division method is 23.2 approximately.

Is Square Root of 540 Irrational?

The actual value of √540 is undetermined. The value of √540 up to 25 decimal places is 23.23790007724450131107559. Hence, the square root of 540 is an irrational number.

☛ Also Check:

Square Root of 512 - √512 = 22.62742
Square Root of 49 - √49 = 7
Square Root of 676 - √676 = 26
Square Root of 116 - √116 = 10.77033
Square Root of 61 - √61 = 7.81025
Square Root of 96 - √96 = 9.79796
Square Root of 361 - √361 = 19

Square Root of 540 Solved Examples

Example 1: Solve the equation x² − 540 = 0

Solution:

x² - 540 = 0 i.e. x² = 540
x = ±√540
Since the value of the square root of 540 is 23.238,
⇒ x = +√540 or -√540 = 23.238 or -23.238.
Example 2: If the area of an equilateral triangle is 540√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 = 540√3 in²
⇒ a = ±√2160 in
Since length can't be negative,
⇒ a = √2160 = 2 √540
We know that the square root of 540 is 23.238.
⇒ a = 46.476 in
Example 3: If the surface area of a sphere is 2160π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 2160π in²
⇒ r = ±√540 in
Since radius can't be negative,
⇒ r = √540
The square root of 540 is 23.238.
⇒ r = 23.238 in

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FAQs on the Square Root of 540

What is the Value of the Square Root of 540?

The square root of 540 is 23.2379.

Why is the Square Root of 540 an Irrational Number?

Upon prime factorizing 540 i.e. 2² × 3³ × 5¹, 3 is in odd power. Therefore, the square root of 540 is irrational.

Evaluate 17 plus 12 square root 540

The given expression is 17 + 12 √540. We know that the square root of 540 is 23.238. Therefore, 17 + 12 √540 = 17 + 12 × 23.238 = 17 + 278.855 = 295.855

If the Square Root of 540 is 23.238. Find the Value of the Square Root of 5.4.

Let us represent √5.4 in p/q form i.e. √(540/100) = 5.4/10 = 2.324. Hence, the value of √5.4 = 2.324

What is the Square Root of 540 in Simplest Radical Form?

We need to express 540 as the product of its prime factors i.e. 540 = 2 × 2 × 3 × 3 × 3 × 5. Therefore, √540 = √2 × 2 × 3 × 3 × 3 × 5 = 6 √15. Thus, the square root of 540 in the lowest radical form is 6 √15.

What is the Square Root of -540?

The square root of -540 is an imaginary number. It can be written as √-540 = √-1 × √540 = i √540 = 23.237i
where i = √-1 and it is called the imaginary unit.

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