Square Root of 4800
The square root of 4800 is expressed as √4800 in the radical form and as (4800)^{½} or (4800)^{0.5} in the exponent form. The square root of 4800 rounded up to 9 decimal places is 69.282032303. It is the positive solution of the equation x^{2} = 4800. We can express the square root of 4800 in its lowest radical form as 40 √3.
 Square Root of 4800: 69.2820323027551
 Square Root of 4800 in exponential form: (4800)^{½} or (4800)^{0.5}
 Square Root of 4800 in radical form: √4800 or 40 √3
1.  What is the Square Root of 4800? 
2.  How to find the Square Root of 4800? 
3.  Is the Square Root of 4800 Irrational? 
4.  FAQs 
What is the Square Root of 4800?
The square root of 4800, (or root 4800), is the number which when multiplied by itself gives the product as 4800. Therefore, the square root of 4800 = √4800 = 40 √3 = 69.2820323027551.
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How to Find Square Root of 4800?
Value of √4800 by Long Division Method
Explanation:
 Forming pairs: 48 and 00
 Find a number Y (6) such that whose square is <= 48. Now divide 48 by 6 with quotient as 6.
 Bring down the next pair 00, to the right of the remainder 12. The new dividend is now 1200.
 Add the last digit of the quotient (6) to the divisor (6) i.e. 6 + 6 = 12. To the right of 12, find a digit Z (which is 9) such that 12Z × Z <= 1200. After finding Z, together 12 and Z (9) form a new divisor 129 for the new dividend 1200.
 Divide 1200 by 129 with the quotient as 9, giving the remainder = 1200  129 × 9 = 1200  1161 = 39.
 Now, let's find the decimal places after the quotient 69.
 Bring down 00 to the right of this remainder 39. The new dividend is now 3900.
 Add the last digit of quotient to divisor i.e. 9 + 129 = 138. To the right of 138, find a digit Z (which is 2) such that 138Z × Z <= 3900. Together they form a new divisor (1382) for the new dividend (3900).
 Divide 3900 by 1382 with the quotient as 2, giving the remainder = 3900  1382 × 2 = 3900  2764 = 1136.
 Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 4800.
Therefore, the square root of 4800 by long division method is 69.2 approximately.
Is Square Root of 4800 Irrational?
The actual value of √4800 is undetermined. The value of √4800 up to 25 decimal places is 69.28203230275509174109785. Hence, the square root of 4800 is an irrational number.
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Square Root of 4800 Solved Examples

Example 1: Solve the equation x^{2} − 4800 = 0
Solution:
x^{2}  4800 = 0 i.e. x^{2} = 4800
x = ±√4800
Since the value of the square root of 4800 is 69.282,
⇒ x = +√4800 or √4800 = 69.282 or 69.282. 
Example 2: If the area of an equilateral triangle is 4800√3 in^{2}. 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)a^{2} = 4800√3 in^{2}
⇒ a = ±√19200 in
Since length can't be negative,
⇒ a = √19200 = 2 √4800
We know that the square root of 4800 is 69.282.
⇒ a = 138.564 in 
Example 3: If the surface area of a cube is 28800 in^{2}. 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 = 6a^{2} = 28800 in^{2}
⇒ a = ±√4800 in
Since length can't be negative,
⇒ a = √4800
We know that the square root of 4800 is 69.282.
⇒ a = 69.282 in
FAQs on the Square Root of 4800
What is the Value of the Square Root of 4800?
The square root of 4800 is 69.28203.
Why is the Square Root of 4800 an Irrational Number?
Upon prime factorizing 4800 i.e. 2^{6} × 3^{1} × 5^{2}, 3 is in odd power. Therefore, the square root of 4800 is irrational.
What is the Square Root of 4800 in Simplest Radical Form?
We need to express 4800 as the product of its prime factors i.e. 4800 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 5 × 5. Therefore, √4800 = √2 × 2 × 2 × 2 × 2 × 2 × 3 × 5 × 5 = 40 √3. Thus, the square root of 4800 in the lowest radical form is 40 √3.
If the Square Root of 4800 is 69.282. Find the Value of the Square Root of 48.
Let us represent √48 in p/q form i.e. √(4800/100) = 48/10 = 6.928. Hence, the value of √48.0 = 6.928
What is the Square of the Square Root of 4800?
The square of the square root of 4800 is the number 4800 itself i.e. (√4800)^{2} = (4800)^{2/2} = 4800.
Is the number 4800 a Perfect Square?
The prime factorization of 4800 = 2^{6} × 3^{1} × 5^{2}. Here, the prime factor 3 is not in the pair. Therefore, 4800 is not a perfect square.
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