The given expression is 8 + 11 √4500. We know that the square root of 4500 is 67.082. Therefore, 8 + 11 √4500 = 8 + 11 × 67.082 = 8 + 737.902 = 745.902

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Let 'a' be the length of the side of the cube. ⇒ Area of the cube = 6a2 = 27000 in2 ⇒ a = ±√4500 in Since length can't be negative, ⇒ a = √4500 We know that the square root of 4500 is 67.082. ⇒ a = 67.082 in

The actual value of √4500 is undetermined. The value of √4500 up to 25 decimal places is 67.08203932499369089227521. Hence, the square root of 4500 is an irrational number.

The square root of -4500 is an imaginary number. It can be written as √-4500 = √-1 × √4500 = i √4500 = 67.082i where i = √-1 and it is called the imaginary unit.

The square root of 4500, (or root 4500), is the number which when multiplied by itself gives the product as 4500. Therefore, the square root of 4500 = √4500 = 30 √5 = 67.08203932499369.

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Let 'a' be the length of the side of the square. ⇒ Area of the square = a2 = 4500 in2 ⇒ a = ±√4500 in Since length can't be negative, ⇒ a = √4500 = 67.082 in

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The prime factorization of 4500 = 22 × 32 × 53. Here, the prime factor 5 is not in the pair. Therefore, 4500 is not a perfect square.

The square root of 4500 is expressed as √4500 in the radical form and as (4500)½ or (4500)0.5 in the exponent form. The square root of 4500 rounded up to 7 decimal places is 67.0820393. It is the positive solution of the equation x2 = 4500. We can express the square root of 4500 in its lowest radical form as 30 √5.

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x2 - 4500 = 0 i.e. x2 = 4500 x = ±√4500 Since the value of the square root of 4500 is 67.082, ⇒ x = +√4500 or -√4500 = 67.082 or -67.082.

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