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Square Root of 720

The square root of 720 is expressed as √720 in the radical form and as (720)^½ or (720)^0.5 in the exponent form. The square root of 720 rounded up to 6 decimal places is 26.832816. It is the positive solution of the equation x² = 720. We can express the square root of 720 in its lowest radical form as 12 √5.

Square Root of 720: 26.832815729997478
Square Root of 720 in exponential form: (720)^½ or (720)^0.5
Square Root of 720 in radical form: √720 or 12 √5

Square Root of 720

1.	What is the Square Root of 720?
2.	How to find the Square Root of 720?
3.	Is the Square Root of 720 Irrational?
4.	FAQs

What is the Square Root of 720?

The square root of 720, (or root 720), is the number which when multiplied by itself gives the product as 720. Therefore, the square root of 720 = √720 = 12 √5 = 26.832815729997478.

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How to Find Square Root of 720?

Square Root of 720 by Long Division Method

Value of √720 by Long Division Method

Explanation:

Forming pairs: 07 and 20
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 20, to the right of the remainder 3. The new dividend is now 320.
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 <= 320. After finding Z, together 4 and Z (6) form a new divisor 46 for the new dividend 320.
Divide 320 by 46 with the quotient as 6, giving the remainder = 320 - 46 × 6 = 320 - 276 = 44.
Now, let's find the decimal places after the quotient 26.
Bring down 00 to the right of this remainder 44. The new dividend is now 4400.
Add the last digit of quotient to divisor i.e. 6 + 46 = 52. To the right of 52, find a digit Z (which is 8) such that 52Z × Z <= 4400. Together they form a new divisor (528) for the new dividend (4400).
Divide 4400 by 528 with the quotient as 8, giving the remainder = 4400 - 528 × 8 = 4400 - 4224 = 176.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 720.

Therefore, the square root of 720 by long division method is 26.8 approx.

Is Square Root of 720 Irrational?

The actual value of √720 is undetermined. The value of √720 up to 25 decimal places is 26.83281572999747635691008. Hence, the square root of 720 is an irrational number.

☛ Also Check:

Square Root of 98 - √98 = 9.89949
Square Root of 28 - √28 = 5.29150
Square Root of 192 - √192 = 13.85641
Square Root of 89 - √89 = 9.43398
Square Root of 65 - √65 = 8.06226
Square Root of 841 - √841 = 29
Square Root of 19 - √19 = 4.35890

Square Root of 720 Solved Examples

Example 1: Solve the equation x² − 720 = 0

Solution:

x² - 720 = 0 i.e. x² = 720
x = ±√720
Since the value of the square root of 720 is 26.833,
⇒ x = +√720 or -√720 = 26.833 or -26.833.
Example 2: If the area of a circle is 720π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 720π in²
⇒ r = ±√720 in
Since radius can't be negative,
⇒ r = √720
The square root of 720 is 26.833.
⇒ r = 26.833 in
Example 3: If the surface area of a cube is 4320 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 = 4320 in²
⇒ a = ±√720 in
Since length can't be negative,
⇒ a = √720
We know that the square root of 720 is 26.833.
⇒ a = 26.833 in

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FAQs on the Square Root of 720

What is the Value of the Square Root of 720?

The square root of 720 is 26.83281.

Why is the Square Root of 720 an Irrational Number?

Upon prime factorizing 720 i.e. 2⁴ × 3² × 5¹, 5 is in odd power. Therefore, the square root of 720 is irrational.

If the Square Root of 720 is 26.833. Find the Value of the Square Root of 7.2.

Let us represent √7.2 in p/q form i.e. √(720/100) = 7.2/10 = 2.683. Hence, the value of √7.2 = 2.683

Evaluate 4 plus 6 square root 720

The given expression is 4 + 6 √720. We know that the square root of 720 is 26.833. Therefore, 4 + 6 √720 = 4 + 6 × 26.833 = 4 + 160.997 = 164.997

Is the number 720 a Perfect Square?

The prime factorization of 720 = 2⁴ × 3² × 5¹. Here, the prime factor 5 is not in the pair. Therefore, 720 is not a perfect square.

What is the Square Root of -720?

The square root of -720 is an imaginary number. It can be written as √-720 = √-1 × √720 = i √720 = 26.832i
where i = √-1 and it is called the imaginary unit.

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