Square Root of 45 Simplified Calculator

What is the square root of 45?

The square root of 45 is a number that, when multiplied by itself, equals 45. In mathematical terms, if x is the square root of 45, then x² = 45. The square root of 45 is approximately 6.708203932499369.

Square roots can be simplified when the radicand (the number under the square root) has perfect square factors. Simplifying square roots makes them easier to work with in mathematical operations.

How to simplify √45

To simplify √45, follow these steps:

1. Factor 45 into its prime factors.
2. Identify any perfect square factors.
3. Take the square root of the perfect square factor(s) and multiply by the remaining factors.

Step-by-step simplification

1. Factor 45:

45 = 9 × 5

9 is a perfect square (3 × 3), and 5 is a prime number.

2. Rewrite the square root using these factors:

√45 = √(9 × 5)

3. Separate the square root of the perfect square:

√(9 × 5) = √9 × √5

4. Simplify √9 to 3:

√9 × √5 = 3√5

This simplified form shows that the square root of 45 can be expressed as 3 times the square root of 5.

Examples of simplified square roots

Here are some examples of square roots simplified to their simplest radical form:

• √45 = 3√5
• √80 = 4√5
• √128 = 8√2
• √180 = 6√5
• √200 = 10√2

These examples show how simplifying square roots can make them more manageable in mathematical calculations.