Square Root of 4500 - How to Find Square Root of 4500? [Solved] (2024)

Table of Contents

What is the Square Root of 4500? How to Find Square Root of 4500? Value of √4500 by Long Division Method Is Square Root of 4500 Irrational? Square Root of 4500 Solved Examples FAQs on the Square Root of 4500 What is the Value of the Square Root of 4500? Why is the Square Root of 4500 an Irrational Number? What is the Square Root of -4500? Is the number 4500 a Perfect Square? If the Square Root of 4500 is 67.082. Find the Value of the Square Root of 45. Evaluate 8 plus 11 square root 4500 FAQs References

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

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.

☛ Check: Square Root Calculator

How to Find Square Root of 4500?

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.
See Also
Multiples of 4500 | Thinkster Math
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

FAQs

Square Root of 4500 - How to Find Square Root of 4500? [Solved]? ›

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 solve √ 4500? ›

For example, the square root of 25 is equal to 5, because 5 x 5 = 25. Expressed in a radical form: √25 = 5. Therefore, solving for the Square Root of 4500, we find that the square root of 4500 is 67.082. Always remember: your answer can be either a whole number or a decimal.

How do you find the square root answer? ›

Here are the steps to finding the square root using factoring:

Find the factors. Factors are the numbers you multiply to find the total under the square root symbol. ...
Separate the factors into their own square roots. ...
Solve for the individual squares. ...
Finish solving the equation.

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How do you solve square root problems without a calculator? ›

To find a square root of a number without a calculator, see if you can get to that whole number by squaring smaller numbers, or multiplying a smaller number by itself. If the number is a perfect square, you will get a whole number as the square root.

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What are the factors of 4500? ›

The factors of 4500 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 125, 150, 180, 225, 250, 300, 375, 450, 500, 750, 900, 1125, 1500, 2250, 4500 and its negative factors are -1, -2, -3, -4, -5, -6, -9, -10, -12, -15, -18, -20, -25, -30, -36, -45, -50, -60, -75, -90, -100, -125, -150, ...

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How to calculate square root by hand? ›

How to find the square root of a number and calculate it by hand

STEP 1: Separate The Digits Into Pairs. To begin, let's organize the workspace. ...
STEP 2: Find The Largest Integer. ...
STEP 3: Now Subtract That Integer. ...
STEP 4: Let's Move To The Next Pair. ...
STEP 5: Find The Right Match. ...
STEP 6: Subtract Again.

Feb 7, 2020

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How do I solve using the square root method? ›

To solve an equation by using the square root property, you will first isolate the term that contains the squared variable. You can then take the square root of both sides and solve for the variable. Make sure to write the final answer in simplified form.

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How is √2 solved? ›

√2 = 1.41421356237309504880168872420969807856967187537694…

For general use, its value is truncated and is used as 1.414 to make calculations easy. The fraction 99/70 is also sometimes used as the value of √2.

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How do you estimate square roots quickly? ›

Step One - Determine which two perfect squares your number falls between. The answer you are looking for will fall between these two numbers. Step Two - Take a guess about the number just after the decimal place. Step Three - Divide the number whose square root you are trying to determine by your guess.

How to calculate square roots in your head? ›

Estimation Method

Choose a nearby guess. For example, \sqrt{59.6} \approx 8.
Calculate the difference between guess² and the number you want to square-root. For example, 8^2 – 59.6 = 4.4.
Divide it by twice your original guess. ...
Add or subtract the correction from the guess to get the estimate of 8 – 0.275 = 7.725.

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How to solve √ 4100? ›

What is the Square Root of 4100? The square root of 4100, (or root 4100), is the number which when multiplied by itself gives the product as 4100. Therefore, the square root of 4100 = √4100 = 10 √41 = 64.03124237432849.

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How to find the square root of 450? ›

What is the Square Root of 450 in Simplest Radical Form? We need to express 450 as the product of its prime factors i.e. 450 = 2 × 3 × 3 × 5 × 5. Therefore, √450 = √2 × 3 × 3 × 5 × 5 = 15 √2. Thus, the square root of 450 in the lowest radical form is 15 √2.

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How is √ calculated? ›

Here, '√' is the radical symbol used to represent the root of numbers. The positive number, when multiplied by itself, represents the square of the number. The square root of the square of a positive number gives the original number. For example, the square of 3 is 9, 3² = 9 and the square root of 9, √9 = 3.

How do you find the value of √? ›

What is the Formula for Calculating the Square Root of a Number? The square root of any number can be expressed using the formula: √y = y^½. In other words, if a number has 1/2 as its exponent, it means we need to find the square root of the number.