Square Root of 724

The square root of 724 is expressed as √724 in the radical form and as (724)^½ or (724)^0.5 in the exponent form. The square root of 724 rounded up to 7 decimal places is 26.9072481. It is the positive solution of the equation x² = 724. We can express the square root of 724 in its lowest radical form as 2 √181.

Square Root of 724: 26.90724809414742
Square Root of 724 in exponential form: (724)^½ or (724)^0.5
Square Root of 724 in radical form: √724 or 2 √181

Square Root of 724

1.	What is the Square Root of 724?
2.	How to find the Square Root of 724?
3.	Is the Square Root of 724 Irrational?
4.	FAQs

What is the Square Root of 724?

The square root of 724, (or root 724), is the number which when multiplied by itself gives the product as 724. Therefore, the square root of 724 = √724 = 2 √181 = 26.90724809414742.

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How to Find Square Root of 724?

Square Root of 724 by Long Division Method

Value of √724 by Long Division Method

Explanation:

Forming pairs: 07 and 24
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 24, to the right of the remainder 3. The new dividend is now 324.
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 <= 324. After finding Z, together 4 and Z (6) form a new divisor 46 for the new dividend 324.
Divide 324 by 46 with the quotient as 6, giving the remainder = 324 - 46 × 6 = 324 - 276 = 48.
Now, let's find the decimal places after the quotient 26.
Bring down 00 to the right of this remainder 48. The new dividend is now 4800.
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 <= 4800. Together they form a new divisor (529) for the new dividend (4800).
Divide 4800 by 529 with the quotient as 9, giving the remainder = 4800 - 529 × 9 = 4800 - 4761 = 39.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 724.

Therefore, the square root of 724 by long division method is 26.9 approx.

Is Square Root of 724 Irrational?

The actual value of √724 is undetermined. The value of √724 up to 25 decimal places is 26.90724809414742063432617. Hence, the square root of 724 is an irrational number.

☛ Also Check:

Square Root of 22 - √22 = 4.69042
Square Root of 841 - √841 = 29
Square Root of 85 - √85 = 9.21954
Square Root of 116 - √116 = 10.77033
Square Root of 61 - √61 = 7.81025
Square Root of 113 - √113 = 10.63015
Square Root of 96 - √96 = 9.79796

Square Root of 724 Solved Examples

Example 1: Solve the equation x² − 724 = 0

Solution:

x² - 724 = 0 i.e. x² = 724
x = ±√724
Since the value of the square root of 724 is 26.907,
⇒ x = +√724 or -√724 = 26.907 or -26.907.
Example 2: If the surface area of a cube is 4344 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 = 4344 in²
⇒ a = ±√724 in
Since length can't be negative,
⇒ a = √724
We know that the square root of 724 is 26.907.
⇒ a = 26.907 in
Example 3: If the area of a circle is 724π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 724π in²
⇒ r = ±√724 in
Since radius can't be negative,
⇒ r = √724
The square root of 724 is 26.907.
⇒ r = 26.907 in

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FAQs on the Square Root of 724

What is the Value of the Square Root of 724?

The square root of 724 is 26.90724.

Why is the Square Root of 724 an Irrational Number?

Upon prime factorizing 724 i.e. 2² × 181¹, 181 is in odd power. Therefore, the square root of 724 is irrational.

What is the Value of 5 square root 724?

The square root of 724 is 26.907. Therefore, 5 √724 = 5 × 26.907 = 134.536.

Is the number 724 a Perfect Square?

The prime factorization of 724 = 2² × 181¹. Here, the prime factor 181 is not in the pair. Therefore, 724 is not a perfect square.

What is the Square Root of 724 in Simplest Radical Form?

We need to express 724 as the product of its prime factors i.e. 724 = 2 × 2 × 181. Therefore, √724 = √2 × 2 × 181 = 2 √181. Thus, the square root of 724 in the lowest radical form is 2 √181.

If the Square Root of 724 is 26.907. Find the Value of the Square Root of 7.24.

Let us represent √7.24 in p/q form i.e. √(724/100) = 7.24/10 = 2.691. Hence, the value of √7.24 = 2.691

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