Hola, iam Rafael Webster, I bid you good day, sir/ma’am.
Hey there! Trying to simplify the square root of 180? Don’t worry, it’s easier than it looks. Let’s break it down and see what we can do. First off, let’s take a look at the prime factorization of 180: 2 x 2 x 3 x 3 x 5 = 180. Now, if we take the square root of each factor, we get 2√2 x 3√3 x 5√5 = 10√30. And that’s it - you’ve simplified the square root of 180! Pretty cool, huh?
How Do You Simplify The Square Root Of 180? [Solved]
Wow, that’s a mouthful! Basically, the square root of 180 is 13.41 and it’s an irrational number.
Understand the Square Root: The square root of a number is the number that, when multiplied by itself, equals the original number. In this case, the square root of 180 is being sought.
Factorize 180: To simplify a square root, it must first be factored into its prime factors. In this case, 180 can be factored into 2 x 2 x 3 x 3 x 5 = 180.
Identify Perfect Squares: Perfect squares are numbers that can be expressed as a whole number multiplied by itself (e.g., 4 x 4 = 16). In this case, 2 x 2 and 3 x 3 are perfect squares and can be simplified further to their roots (2 and 3).
Simplify Remaining Factors: The remaining factors in this equation are 5 and 1 (180/2/2/3/3 = 5). Since these cannot be simplified further they remain in the equation as-is (5x1=5).
Final Answer: The final answer for simplifying the square root of 180 is therefore √180 = √(2x2x3x3x5) = 2√(3x5) = 6√5
Well, simplifying the square root of 180 is pretty easy - it’s just 15! Ain’t that a cinch?
