What is the square root of 360?
Understand the Problem
The question is asking for the square root of 360. To find the square root, we typically look for a number that, when multiplied by itself, gives us 360. This can be done using a calculator or simplifying the expression to find the exact value or an approximate decimal.
Answer
$6\sqrt{10} \approx 18.972$
Answer for screen readers
The exact square root of 360 is $6\sqrt{10}$ and the approximate decimal value is $18.972$.
Steps to Solve

Simplifying the number under the square root
To simplify $\sqrt{360}$, we can factor 360 into its prime factors:
$$ 360 = 36 \times 10 = 6^2 \times 10 $$ 
Using the property of square roots
Using the property of square roots that states $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$, we can rewrite our expression:
$$ \sqrt{360} = \sqrt{36 \times 10} = \sqrt{36} \times \sqrt{10} $$ 
Calculating the square roots
Now we can calculate the square root of 36 and multiply by the square root of 10:
$$ \sqrt{36} = 6 $$
So,
$$ \sqrt{360} = 6 \times \sqrt{10} $$ 
Approximating the value
To find an approximate decimal value for $\sqrt{10}$, we can use a calculator:
$$ \sqrt{10} \approx 3.162 $$
Thus,
$$ \sqrt{360} \approx 6 \times 3.162 \approx 18.972 $$
The exact square root of 360 is $6\sqrt{10}$ and the approximate decimal value is $18.972$.
More Information
The value $6\sqrt{10}$ represents the exact square root of 360, while 18.972 is an approximation. The square root of a number can often be simplified using its prime factors, making calculations easier.
Tips
 Mistaking the approximation of square roots can lead to incorrect answers. Always check the value of the square root using a calculator for better accuracy.