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Square Root of 4500

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.

Square Root of 4500: 67.08203932499369
Square Root of 4500 in exponential form: (4500)^½ or (4500)^0.5
Square Root of 4500 in radical form: √4500 or 30 √5

Square Root of 4500

1.	What is the Square Root of 4500?
2.	How to find the Square Root of 4500?
3.	Is the Square Root of 4500 Irrational?
4.	FAQs

What is the Square Root of 4500?

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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How to Find Square Root of 4500?

Square Root of 4500 by Long Division Method

Value of √4500 by Long Division Method

Explanation:

Forming pairs: 45 and 00
Find a number Y (6) such that whose square is <= 45. Now divide 45 by 6 with quotient as 6.
Bring down the next pair 00, to the right of the remainder 9. The new dividend is now 900.
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 7) such that 12Z × Z <= 900. After finding Z, together 12 and Z (7) form a new divisor 127 for the new dividend 900.
Divide 900 by 127 with the quotient as 7, giving the remainder = 900 - 127 × 7 = 900 - 889 = 11.
Now, let's find the decimal places after the quotient 67.
Bring down 00 to the right of this remainder 11. The new dividend is now 1100.
Add the last digit of quotient to divisor i.e. 7 + 127 = 134. To the right of 134, find a digit Z (which is 0) such that 134Z × Z <= 1100. Together they form a new divisor (1340) for the new dividend (1100).
Divide 1100 by 1340 with the quotient as 0, giving the remainder = 1100 - 1340 × 0 = 1100 - 0 = 1100.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 4500.

Therefore, the square root of 4500 by long division method is 67.0 approximately.

Is Square Root of 4500 Irrational?

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.

☛ Also Check:

Square Root of 51 - √51 = 7.14143
Square Root of 49 - √49 = 7
Square Root of 676 - √676 = 26
Square Root of 140 - √140 = 11.83216
Square Root of 169 - √169 = 13
Square Root of 41 - √41 = 6.40312
Square Root of 200 - √200 = 14.14214

Square Root of 4500 Solved Examples

Example 1: Solve the equation x² − 4500 = 0

Solution:

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.
Example 2: If the surface area of a cube is 27000 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 = 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
Example 3: If the area of a square is 4500 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 = 4500 in²
⇒ a = ±√4500 in
Since length can't be negative,
⇒ a = √4500 = 67.082 in

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FAQs on the Square Root of 4500

What is the Value of the Square Root of 4500?

The square root of 4500 is 67.08203.

Why is the Square Root of 4500 an Irrational Number?

Upon prime factorizing 4500 i.e. 2² × 3² × 5³, 5 is in odd power. Therefore, the square root of 4500 is irrational.

What is the Square Root of -4500?

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.

Is the number 4500 a Perfect Square?

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.

If the Square Root of 4500 is 67.082. Find the Value of the Square Root of 45.

Let us represent √45 in p/q form i.e. √(4500/100) = 45/10 = 6.708. Hence, the value of √45.0 = 6.708

Evaluate 8 plus 11 square root 4500

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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