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Square Root of 728

The square root of 728 is expressed as √728 in the radical form and as (728)^½ or (728)^0.5 in the exponent form. The square root of 728 rounded up to 7 decimal places is 26.9814751. It is the positive solution of the equation x² = 728. We can express the square root of 728 in its lowest radical form as 2 √182.

Square Root of 728: 26.981475126464083
Square Root of 728 in exponential form: (728)^½ or (728)^0.5
Square Root of 728 in radical form: √728 or 2 √182

Square Root of 728

1.	What is the Square Root of 728?
2.	How to find the Square Root of 728?
3.	Is the Square Root of 728 Irrational?
4.	FAQs

What is the Square Root of 728?

The square root of 728, (or root 728), is the number which when multiplied by itself gives the product as 728. Therefore, the square root of 728 = √728 = 2 √182 = 26.981475126464083.

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How to Find Square Root of 728?

Square Root of 728 by Long Division Method

Value of √728 by Long Division Method

Explanation:

Forming pairs: 07 and 28
Find a number Y (2) such that whose square is <= 7. Now divide 07 by 2 with quotient as 2.
Bring down the next pair 28, to the right of the remainder 3. The new dividend is now 328.
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 6) such that 4Z × Z <= 328. After finding Z, together 4 and Z (6) form a new divisor 46 for the new dividend 328.
Divide 328 by 46 with the quotient as 6, giving the remainder = 328 - 46 × 6 = 328 - 276 = 52.
Now, let's find the decimal places after the quotient 26.
Bring down 00 to the right of this remainder 52. The new dividend is now 5200.
Add the last digit of quotient to divisor i.e. 6 + 46 = 52. To the right of 52, find a digit Z (which is 9) such that 52Z × Z <= 5200. Together they form a new divisor (529) for the new dividend (5200).
Divide 5200 by 529 with the quotient as 9, giving the remainder = 5200 - 529 × 9 = 5200 - 4761 = 439.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 728.

Therefore, the square root of 728 by long division method is 26.9 approximately.

Is Square Root of 728 Irrational?

The actual value of √728 is undetermined. The value of √728 up to 25 decimal places is 26.98147512646408293110061. Hence, the square root of 728 is an irrational number.

☛ Also Check:

Square Root of 49 - √49 = 7
Square Root of 2 - √2 = 1.41421
Square Root of 113 - √113 = 10.63015
Square Root of 11 - √11 = 3.31662
Square Root of 324 - √324 = 18
Square Root of 17 - √17 = 4.12311
Square Root of 512 - √512 = 22.62742

Square Root of 728 Solved Examples

Example 1: Solve the equation x² − 728 = 0

Solution:

x² - 728 = 0 i.e. x² = 728
x = ±√728
Since the value of the square root of 728 is 26.981,
⇒ x = +√728 or -√728 = 26.981 or -26.981.
Example 2: If the area of a circle is 728π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 728π in²
⇒ r = ±√728 in
Since radius can't be negative,
⇒ r = √728
The square root of 728 is 26.981.
⇒ r = 26.981 in
Example 3: If the area of an equilateral triangle is 728√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 = 728√3 in²
⇒ a = ±√2912 in
Since length can't be negative,
⇒ a = √2912 = 2 √728
We know that the square root of 728 is 26.981.
⇒ a = 53.963 in

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FAQs on the Square Root of 728

What is the Value of the Square Root of 728?

The square root of 728 is 26.98147.

Why is the Square Root of 728 an Irrational Number?

Upon prime factorizing 728 i.e. 2³ × 7¹ × 13¹, 2 is in odd power. Therefore, the square root of 728 is irrational.

Evaluate 12 plus 3 square root 728

The given expression is 12 + 3 √728. We know that the square root of 728 is 26.981. Therefore, 12 + 3 √728 = 12 + 3 × 26.981 = 12 + 80.944 = 92.944

What is the Square Root of 728 in Simplest Radical Form?

We need to express 728 as the product of its prime factors i.e. 728 = 2 × 2 × 2 × 7 × 13. Therefore, √728 = √2 × 2 × 2 × 7 × 13 = 2 √182. Thus, the square root of 728 in the lowest radical form is 2 √182.

What is the Square of the Square Root of 728?

The square of the square root of 728 is the number 728 itself i.e. (√728)² = (728)^2/2 = 728.

If the Square Root of 728 is 26.981. Find the Value of the Square Root of 7.28.

Let us represent √7.28 in p/q form i.e. √(728/100) = 7.28/10 = 2.698. Hence, the value of √7.28 = 2.698

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