Square Root of 30
Calculate √30 instantly — exact value, step-by-step explanation, and properties.
How to Calculate √30
The square root of 30 is approximately 5.4772255751. Since 30 is not a perfect square, its square root is an irrational number. We know that √25 = 5 and √36 = 6, so √30 falls between 5 and 6. To estimate manually: start with 5.4, then refine using the Babylonian method — guess a value, divide 30 by it, average the result with your guess, and repeat.
The Babylonian Method (Step by Step)
- Start with an initial guess. Since √25 = 5 and √36 = 6, a good starting guess is 5.5.
- Divide 30 by your guess: 30 ÷ 5.5 = 5.4545
- Average the result with your guess: (5.5 + 5.4545) ÷ 2 = 5.477273
- Repeat with the new estimate until you reach the desired precision.
√30 ≈ 5.4772255751 Properties of √30
Perfect Square?
No
30 is not a perfect square. Its root is irrational.
Decimal Value
5.4772255751
Rounded to 10 decimal places.
Square Root Symbol
√30
Also written as 30^(1/2) or 30^0.5 in programming.
Related Square Root Values
Reference table of square roots near 30 for quick comparison.
Frequently Asked Questions
What is the square root of 30?
The square root of 30 is approximately 5.4772255751. This is an irrational number.
Is 30 a perfect square?
No, 30 is not a perfect square. Its square root (5.4772255751...) is an irrational number that cannot be expressed as a simple fraction.
How do you calculate √30 by hand?
To calculate √30 by hand, use the Babylonian method: (1) Make an initial guess — since √25 = 5 and √36 = 6, start with 5.5. (2) Divide 30 by your guess. (3) Average the result with your guess. (4) Repeat steps 2-3 until you reach desired precision.
What is √30 in simplified radical form?
√30 is already in its simplest radical form. The number 30 has no perfect square factors other than 1.