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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 x² = 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.
a² = 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 = 2² × 2 × 3 × 5².
Taking square root on both the sides, we get √600 = √(2 × 2 × 2 × 3 × 5 × 5).
600^½ = ( 2² × 2 × 3 × 5²)^½ = 2 × 5 × (2× 3)^½ = 10 × (6)^½
Hence, √600 = 10√6

Square Root of 600 by the Long Division Method

square root of 600 by 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

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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 600^½in the exponential form and 10√6 in its simplest radical form.
√600 = 24.494
√600 is irrational.

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,
Hypotenuse²= Leg1² + Leg2²
(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
Height² = 625 - 25 = 600
Height = √600

Thus, 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 in². 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)a² = 600√3 in²
⇒ 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

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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. 2³ × 3¹ × 5², 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 = 2³ × 3¹ × 5². 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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