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Square Root of 7200

The square root of 7200 is expressed as √7200 in the radical form and as (7200)^½ or (7200)^0.5 in the exponent form. The square root of 7200 rounded up to 5 decimal places is 84.85281. It is the positive solution of the equation x² = 7200. We can express the square root of 7200 in its lowest radical form as 60 √2.

Square Root of 7200: 84.8528137423857
Square Root of 7200 in exponential form: (7200)^½ or (7200)^0.5
Square Root of 7200 in radical form: √7200 or 60 √2

Square Root of 7200

1.	What is the Square Root of 7200?
2.	How to find the Square Root of 7200?
3.	Is the Square Root of 7200 Irrational?
4.	FAQs

What is the Square Root of 7200?

The square root of 7200, (or root 7200), is the number which when multiplied by itself gives the product as 7200. Therefore, the square root of 7200 = √7200 = 60 √2 = 84.8528137423857.

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How to Find Square Root of 7200?

Square Root of 7200 by Long Division Method

Value of √7200 by Long Division Method

Explanation:

Forming pairs: 72 and 00
Find a number Y (8) such that whose square is <= 72. Now divide 72 by 8 with quotient as 8.
Bring down the next pair 00, to the right of the remainder 8. The new dividend is now 800.
Add the last digit of the quotient (8) to the divisor (8) i.e. 8 + 8 = 16. To the right of 16, find a digit Z (which is 4) such that 16Z × Z <= 800. After finding Z, together 16 and Z (4) form a new divisor 164 for the new dividend 800.
Divide 800 by 164 with the quotient as 4, giving the remainder = 800 - 164 × 4 = 800 - 656 = 144.
Now, let's find the decimal places after the quotient 84.
Bring down 00 to the right of this remainder 144. The new dividend is now 14400.
Add the last digit of quotient to divisor i.e. 4 + 164 = 168. To the right of 168, find a digit Z (which is 8) such that 168Z × Z <= 14400. Together they form a new divisor (1688) for the new dividend (14400).
Divide 14400 by 1688 with the quotient as 8, giving the remainder = 14400 - 1688 × 8 = 14400 - 13504 = 896.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 7200.

Therefore, the square root of 7200 by long division method is 84.8 approximately.

Is Square Root of 7200 Irrational?

The actual value of √7200 is undetermined. The value of √7200 up to 25 decimal places is 84.85281374238570292810132. Hence, the square root of 7200 is an irrational number.

☛ Also Check:

Square Root of 125 - √125 = 11.18034
Square Root of 72 - √72 = 8.48528
Square Root of 225 - √225 = 15
Square Root of 325 - √325 = 18.02776
Square Root of 1024 - √1024 = 32
Square Root of 48 - √48 = 6.92820
Square Root of 39 - √39 = 6.24500

Square Root of 7200 Solved Examples

Example 1: Solve the equation x² − 7200 = 0

Solution:

x² - 7200 = 0 i.e. x² = 7200
x = ±√7200
Since the value of the square root of 7200 is 84.853,
⇒ x = +√7200 or -√7200 = 84.853 or -84.853.
Example 2: If the surface area of a cube is 43200 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 = 43200 in²
⇒ a = ±√7200 in
Since length can't be negative,
⇒ a = √7200
We know that the square root of 7200 is 84.853.
⇒ a = 84.853 in
Example 3: If the area of a square is 7200 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 = 7200 in²
⇒ a = ±√7200 in
Since length can't be negative,
⇒ a = √7200 = 84.853 in

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FAQs on the Square Root of 7200

What is the Value of the Square Root of 7200?

The square root of 7200 is 84.85281.

Why is the Square Root of 7200 an Irrational Number?

Upon prime factorizing 7200 i.e. 2⁵ × 3² × 5², 2 is in odd power. Therefore, the square root of 7200 is irrational.

What is the Square Root of 7200 in Simplest Radical Form?

We need to express 7200 as the product of its prime factors i.e. 7200 = 2 × 2 × 2 × 2 × 2 × 3 × 3 × 5 × 5. Therefore, √7200 = √2 × 2 × 2 × 2 × 2 × 3 × 3 × 5 × 5 = 60 √2. Thus, the square root of 7200 in the lowest radical form is 60 √2.

What is the Value of 18 square root 7200?

The square root of 7200 is 84.853. Therefore, 18 √7200 = 18 × 84.853 = 1527.351.

What is the Square Root of -7200?

The square root of -7200 is an imaginary number. It can be written as √-7200 = √-1 × √7200 = i √7200 = 84.852i
where i = √-1 and it is called the imaginary unit.

Is the number 7200 a Perfect Square?

The prime factorization of 7200 = 2⁵ × 3² × 5². Here, the prime factor 2 is not in the pair. Therefore, 7200 is not a perfect square.

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