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Square Root of 648

The square root of 648 is expressed as √648 in the radical form and as (648)^½ or (648)^0.5 in the exponent form. The square root of 648 rounded up to 5 decimal places is 25.45584. It is the positive solution of the equation x² = 648. We can express the square root of 648 in its lowest radical form as 18 √2.

Square Root of 648: 25.45584412271571
Square Root of 648 in exponential form: (648)^½ or (648)^0.5
Square Root of 648 in radical form: √648 or 18 √2

Square Root of 648

1.	What is the Square Root of 648?
2.	How to find the Square Root of 648?
3.	Is the Square Root of 648 Irrational?
4.	FAQs

What is the Square Root of 648?

The square root of 648, (or root 648), is the number which when multiplied by itself gives the product as 648. Therefore, the square root of 648 = √648 = 18 √2 = 25.45584412271571.

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How to Find Square Root of 648?

Square Root of 648 by Long Division Method

Value of √648 by Long Division Method

Explanation:

Forming pairs: 06 and 48
Find a number Y (2) such that whose square is <= 6. Now divide 06 by 2 with quotient as 2.
Bring down the next pair 48, to the right of the remainder 2. The new dividend is now 248.
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 5) such that 4Z × Z <= 248. After finding Z, together 4 and Z (5) form a new divisor 45 for the new dividend 248.
Divide 248 by 45 with the quotient as 5, giving the remainder = 248 - 45 × 5 = 248 - 225 = 23.
Now, let's find the decimal places after the quotient 25.
Bring down 00 to the right of this remainder 23. The new dividend is now 2300.
Add the last digit of quotient to divisor i.e. 5 + 45 = 50. To the right of 50, find a digit Z (which is 4) such that 50Z × Z <= 2300. Together they form a new divisor (504) for the new dividend (2300).
Divide 2300 by 504 with the quotient as 4, giving the remainder = 2300 - 504 × 4 = 2300 - 2016 = 284.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 648.

Therefore, the square root of 648 by long division method is 25.4 approximately.

Is Square Root of 648 Irrational?

The actual value of √648 is undetermined. The value of √648 up to 25 decimal places is 25.45584412271571087843040. Hence, the square root of 648 is an irrational number.

☛ Also Check:

Square Root of 113 - √113 = 10.63015
Square Root of 162 - √162 = 12.72792
Square Root of 2 - √2 = 1.41421
Square Root of 92 - √92 = 9.59166
Square Root of 320 - √320 = 17.88854
Square Root of 52 - √52 = 7.21110
Square Root of 29 - √29 = 5.38516

Square Root of 648 Solved Examples

Example 1: Solve the equation x² − 648 = 0

Solution:

x² - 648 = 0 i.e. x² = 648
x = ±√648
Since the value of the square root of 648 is 25.456,
⇒ x = +√648 or -√648 = 25.456 or -25.456.
Example 2: If the area of a circle is 648π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 648π in²
⇒ r = ±√648 in
Since radius can't be negative,
⇒ r = √648
The square root of 648 is 25.456.
⇒ r = 25.456 in
Example 3: If the surface area of a cube is 3888 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 = 3888 in²
⇒ a = ±√648 in
Since length can't be negative,
⇒ a = √648
We know that the square root of 648 is 25.456.
⇒ a = 25.456 in

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FAQs on the Square Root of 648

What is the Value of the Square Root of 648?

The square root of 648 is 25.45584.

Why is the Square Root of 648 an Irrational Number?

Upon prime factorizing 648 i.e. 2³ × 3⁴, 2 is in odd power. Therefore, the square root of 648 is irrational.

Evaluate 18 plus 19 square root 648

The given expression is 18 + 19 √648. We know that the square root of 648 is 25.456. Therefore, 18 + 19 √648 = 18 + 19 × 25.456 = 18 + 483.661 = 501.661

What is the Square of the Square Root of 648?

The square of the square root of 648 is the number 648 itself i.e. (√648)² = (648)^2/2 = 648.

What is the Square Root of 648 in Simplest Radical Form?

We need to express 648 as the product of its prime factors i.e. 648 = 2 × 2 × 2 × 3 × 3 × 3 × 3. Therefore, √648 = √2 × 2 × 2 × 3 × 3 × 3 × 3 = 18 √2. Thus, the square root of 648 in the lowest radical form is 18 √2.

What is the Square Root of -648?

The square root of -648 is an imaginary number. It can be written as √-648 = √-1 × √648 = i √648 = 25.455i
where i = √-1 and it is called the imaginary unit.

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