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
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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.
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