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Square Root of 264

The square root of 264 is expressed as √264 in the radical form and as (264)^½ or (264)^0.5 in the exponent form. The square root of 264 rounded up to 8 decimal places is 16.24807681. It is the positive solution of the equation x² = 264. We can express the square root of 264 in its lowest radical form as 2 √66.

Square Root of 264: 16.24807680927192
Square Root of 264 in exponential form: (264)^½ or (264)^0.5
Square Root of 264 in radical form: √264 or 2 √66

Square Root of 264

1.	What is the Square Root of 264?
2.	How to find the Square Root of 264?
3.	Is the Square Root of 264 Irrational?
4.	FAQs

What is the Square Root of 264?

The square root of 264, (or root 264), is the number which when multiplied by itself gives the product as 264. Therefore, the square root of 264 = √264 = 2 √66 = 16.24807680927192.

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How to Find Square Root of 264?

Square Root of 264 by Long Division Method

Value of √264 by Long Division Method

Explanation:

Forming pairs: 02 and 64
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 64, to the right of the remainder 1. The new dividend is now 164.
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 6) such that 2Z × Z <= 164. After finding Z, together 2 and Z (6) form a new divisor 26 for the new dividend 164.
Divide 164 by 26 with the quotient as 6, giving the remainder = 164 - 26 × 6 = 164 - 156 = 8.
Now, let's find the decimal places after the quotient 16.
Bring down 00 to the right of this remainder 8. The new dividend is now 800.
Add the last digit of quotient to divisor i.e. 6 + 26 = 32. To the right of 32, find a digit Z (which is 2) such that 32Z × Z <= 800. Together they form a new divisor (322) for the new dividend (800).
Divide 800 by 322 with the quotient as 2, giving the remainder = 800 - 322 × 2 = 800 - 644 = 156.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 264.

Therefore, the square root of 264 by long division method is 16.2 approx.

Is Square Root of 264 Irrational?

The actual value of √264 is undetermined. The value of √264 up to 25 decimal places is 16.24807680927192072091977. Hence, the square root of 264 is an irrational number.

☛ Also Check:

Square Root of 36 - √36 = 6
Square Root of 80 - √80 = 8.94427
Square Root of 74 - √74 = 8.60233
Square Root of 89 - √89 = 9.43398
Square Root of 72 - √72 = 8.48528
Square Root of 11 - √11 = 3.31662
Square Root of 12 - √12 = 3.46410

Square Root of 264 Solved Examples

Example 1: Solve the equation x² − 264 = 0

Solution:

x² - 264 = 0 i.e. x² = 264
x = ±√264
Since the value of the square root of 264 is 16.248,
⇒ x = +√264 or -√264 = 16.248 or -16.248.
Example 2: If the surface area of a cube is 1584 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 = 1584 in²
⇒ a = ±√264 in
Since length can't be negative,
⇒ a = √264
We know that the square root of 264 is 16.248.
⇒ a = 16.248 in
Example 3: If the area of a circle is 264π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 264π in²
⇒ r = ±√264 in
Since radius can't be negative,
⇒ r = √264
The square root of 264 is 16.248.
⇒ r = 16.248 in

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FAQs on the Square Root of 264

What is the Value of the Square Root of 264?

The square root of 264 is 16.24807.

Why is the Square Root of 264 an Irrational Number?

Upon prime factorizing 264 i.e. 2³ × 3¹ × 11¹, 2 is in odd power. Therefore, the square root of 264 is irrational.

What is the Square Root of -264?

The square root of -264 is an imaginary number. It can be written as √-264 = √-1 × √264 = i √264 = 16.248i
where i = √-1 and it is called the imaginary unit.

What is the Square of the Square Root of 264?

The square of the square root of 264 is the number 264 itself i.e. (√264)² = (264)^2/2 = 264.

If the Square Root of 264 is 16.248. Find the Value of the Square Root of 2.64.

Let us represent √2.64 in p/q form i.e. √(264/100) = 2.64/10 = 1.625. Hence, the value of √2.64 = 1.625

Evaluate 19 plus 4 square root 264

The given expression is 19 + 4 √264. We know that the square root of 264 is 16.248. Therefore, 19 + 4 √264 = 19 + 4 × 16.248 = 19 + 64.992 = 83.992

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