A day full of math games & activities. Find one near you.

Square Root of 1728

The square root of 1728 is expressed as √1728 in the radical form and as (1728)^½ or (1728)^0.5 in the exponent form. The square root of 1728 rounded up to 6 decimal places is 41.569219. It is the positive solution of the equation x² = 1728. We can express the square root of 1728 in its lowest radical form as 24 √3.

Square Root of 1728: 41.569219381653056
Square Root of 1728 in exponential form: (1728)^½ or (1728)^0.5
Square Root of 1728 in radical form: √1728 or 24 √3

Square Root of 1728

1.	What is the Square Root of 1728?
2.	How to find the Square Root of 1728?
3.	Is the Square Root of 1728 Irrational?
4.	FAQs

What is the Square Root of 1728?

The square root of 1728, (or root 1728), is the number which when multiplied by itself gives the product as 1728. Therefore, the square root of 1728 = √1728 = 24 √3 = 41.569219381653056.

☛ Check: Square Root Calculator

How to Find Square Root of 1728?

Square Root of 1728 by Long Division Method

Value of √1728 by Long Division Method

Explanation:

Forming pairs: 17 and 28
Find a number Y (4) such that whose square is <= 17. Now divide 17 by 4 with quotient as 4.
Bring down the next pair 28, to the right of the remainder 1. The new dividend is now 128.
Add the last digit of the quotient (4) to the divisor (4) i.e. 4 + 4 = 8. To the right of 8, find a digit Z (which is 1) such that 8Z × Z <= 128. After finding Z, together 8 and Z (1) form a new divisor 81 for the new dividend 128.
Divide 128 by 81 with the quotient as 1, giving the remainder = 128 - 81 × 1 = 128 - 81 = 47.
Now, let's find the decimal places after the quotient 41.
Bring down 00 to the right of this remainder 47. The new dividend is now 4700.
Add the last digit of quotient to divisor i.e. 1 + 81 = 82. To the right of 82, find a digit Z (which is 5) such that 82Z × Z <= 4700. Together they form a new divisor (825) for the new dividend (4700).
Divide 4700 by 825 with the quotient as 5, giving the remainder = 4700 - 825 × 5 = 4700 - 4125 = 575.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 1728.

Therefore, the square root of 1728 by long division method is 41.5 approximately.

Is Square Root of 1728 Irrational?

The actual value of √1728 is undetermined. The value of √1728 up to 25 decimal places is 41.56921938165305504465871. Hence, the square root of 1728 is an irrational number.

☛ Also Check:

Square Root of 34 - √34 = 5.83095
Square Root of 625 - √625 = 25
Square Root of 89 - √89 = 9.43398
Square Root of 324 - √324 = 18
Square Root of 200 - √200 = 14.14214
Square Root of 113 - √113 = 10.63015
Square Root of 35 - √35 = 5.91608

Square Root of 1728 Solved Examples

Example 1: Solve the equation x² − 1728 = 0

Solution:

x² - 1728 = 0 i.e. x² = 1728
x = ±√1728
Since the value of the square root of 1728 is 41.569,
⇒ x = +√1728 or -√1728 = 41.569 or -41.569.
Example 2: If the surface area of a cube is 10368 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 = 10368 in²
⇒ a = ±√1728 in
Since length can't be negative,
⇒ a = √1728
We know that the square root of 1728 is 41.569.
⇒ a = 41.569 in
Example 3: If the area of a square is 1728 in². Find the length of the side of the square.

Solution:

Let 'a' be the length of the side of the square.
⇒ Area of the square = a² = 1728 in²
⇒ a = ±√1728 in
Since length can't be negative,
⇒ a = √1728 = 41.569 in

go to slide go to slide go to slide

Ready to see the world through math’s eyes?

Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything.

Book a Free Trial Class

FAQs on the Square Root of 1728

What is the Value of the Square Root of 1728?

The square root of 1728 is 41.56921.

Why is the Square Root of 1728 an Irrational Number?

Upon prime factorizing 1728 i.e. 2⁶ × 3³, 3 is in odd power. Therefore, the square root of 1728 is irrational.

Evaluate 11 plus 4 square root 1728

The given expression is 11 + 4 √1728. We know that the square root of 1728 is 41.569. Therefore, 11 + 4 √1728 = 11 + 4 × 41.569 = 11 + 166.277 = 177.277

If the Square Root of 1728 is 41.569. Find the Value of the Square Root of 17.28.

Let us represent √17.28 in p/q form i.e. √(1728/100) = 17.28/10 = 4.157. Hence, the value of √17.28 = 4.157

What is the Value of 17 square root 1728?

The square root of 1728 is 41.569. Therefore, 17 √1728 = 17 × 41.569 = 706.677.

What is the Square of the Square Root of 1728?

The square of the square root of 1728 is the number 1728 itself i.e. (√1728)² = (1728)^2/2 = 1728.

Math worksheets and
visual curriculum