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Square Root of 600
The square root of 600 is expressed as √600 in the radical form and as (600)^{½} or (600)^{0.5} in the exponent form. The square root of 600 rounded up to 5 decimal places is 24.49490. It is the positive solution of the equation x^{2} = 600. We can express the square root of 600 in its lowest radical form as 10 √6.
 Square Root of 600: 24.49489742783178
 Square Root of 600 in exponential form: (600)^{½} or (600)^{0.5}
 Square Root of 600 in radical form: √600 or 10 √6
1.  What Is the Square Root of 600? 
2.  Is Square Root of 600 Rational or Irrational? 
3.  How to Find the Square Root of 600? 
4.  FAQs on Square Root of 600 
What Is the Square Root of 600?
 The square root of 600 is written in the radical form as √600.
 It means then there is a number a such that: a × a = 600.
 a^{2} = 600 ⇒ a = √600. a is the 2nd root of 600.
 24.494 × 24.494 = 600 and 24.494 × 24.494 = 600
 Thus, √600 = ± 24.494
 In the exponential form, we denote √600 as (600) ^{½}
Is Square Root of 600 Rational or Irrational?
√600 cannot be written in the form of p/q, hence it is an irrational number. The square root of 600 is an irrational number where the numbers after the decimal point go up to infinity as √600 = 24.49489742783178.
How to Find the Square Root of 600?
The square root of 600 or any number can be calculated in many ways. A few to mention are the prime factorization method and the long division method.
Square Root of 600 in the simplest radical form
 To express the square root 600 in the simplest radical form, we do the prime factorization of 600 as 600 = 2^{2} × 2 × 3 × 5^{2}.
 Taking square root on both the sides, we get √600 = √(2 × 2 × 2 × 3 × 5 × 5).
 600^{½} = ( 2^{2} × 2 × 3 × 5^{2})^{½} = 2 × 5 × (2× 3)^{½} = 10 × (6)^{½}
 Hence, √600 = 10√6
Square Root of 600 by the Long Division Method
The long division method helps us to find a more accurate value of square root of any number. Let's see how to find the square root of 600 by the long division method.
 Step 1: Express 600 as 6 00. 00 00. We take the number in pairs from the right. Take 6 as the dividend.
 Step 2: Now find a quotient which is the same as the divisor. Multiply quotient and the divisor. 2 × 2 = 4 and subtract the result from 6 and get the remainder as 2.
 Step 3: Bring down the pair of zeros. 2 00 is our new dividend.
 Step 4: Now double the quotient obtained in step 2. Here is 2 × 2 = 4. 40 becomes the new divisor.
 Step 5: We need to choose a number such that (number + 40) × number gives a number ≤ 200. (40 + 4) × 4 = 176
 Step 6: Subtract this from 200. Get the remainder as 24. Get the next pair of zeros down. 24 00 is the new dividend.
 Step 7: Now the quotient is 24. Double it. Here it is 48. 480. Now find a (number + 480) × number that gives ≤ 24 00. We find that 484 × 4 = 1936. Get the remainder as 464.
 Step 8: Repeat the process until we get the square root of 99 approximated to two places. Thus, √600 = 24.494
Explore Square roots using illustrations and interactive examples
Challenging Questions
 What is the least number that has to be multiplied with 600 to make it a perfect square? What is the square root of that perfect square?
 Find the sum of first 25 consecutive odd numbers. Subtract 25 from it. What pattern do you observe?
Important Notes
 The square root of 600 is 600^{½ }in the exponential form and 10√6 in its simplest radical form.
 √600 = 24.494
 √600 is irrational.
Square Root of 600 Solved Examples

Example 1: If the length of the slide in the park is 625 feet and the distance between the slide and the stair case is 25 feet, find the height of the staircase.
Solution:
The height of the stair case, the slide and the distance between them forms a right triangle.
Applying the Pythagorean theorem,
Hypotenuse^{2 }= Leg1^{2} + Leg2^{2}
(Length of the slide)^{2 }= (Height of the staircase)^{2 }+ (Distance between them)^{2}
(Height of the staircase)^{2 }= (Length of the slide)^{2}  (Distance between them)^{2 }
Height^{2} = 625  25 = 600
Height = √600Thus, the height of the staircase = 24.494 feet.

Example 2: Evaluate: √600 × √ 200
Solution:
√600 = 10√6 and √ 200 = 10√2
Thus, √600 × √ 200 = 10√6 × 10√2 = 10 × √6 × 10 × √2 = 100√(6 × 2) = 100√12.
Hence, √600 × √ 200 = 100√12. 
Example: If the area of an equilateral triangle is 600√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} = 600√3 in^{2}
⇒ a = ±√2400 in
Since length can't be negative,
⇒ a = √2400 = 2 √600
We know that the square root of 600 is 24.495.
⇒ a = 48.990 in
FAQs on the Square Root of 600
What is the Value of the Square Root of 600?
The square root of 600 is 24.49489.
Why is the Square Root of 600 an Irrational Number?
Upon prime factorizing 600 i.e. 2^{3} × 3^{1} × 5^{2}, 2 is in odd power. Therefore, the square root of 600 is irrational.
If the Square Root of 600 is 24.495. Find the Value of the Square Root of 6.
Let us represent √6 in p/q form i.e. √(600/100) = 6/10 = 2.449. Hence, the value of √6.0 = 2.449
Evaluate 9 plus 15 square root 600
The given expression is 9 + 15 √600. We know that the square root of 600 is 24.495. Therefore, 9 + 15 √600 = 9 + 15 × 24.495 = 9 + 367.423 = 376.423
Is the number 600 a Perfect Square?
The prime factorization of 600 = 2^{3} × 3^{1} × 5^{2}. Here, the prime factor 2 is not in the pair. Therefore, 600 is not a perfect square.
What is the Square of the Square Root of 600?
The square of the square root of 600 is the number 600 itself i.e. (√600)^{2} = (600)^{2/2} = 600.
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