what is the following product sqrt 30 sqrt 10
Understand the Problem
The question is asking for the product of two square roots: the square root of 30 and the square root of 10. To solve this, we will multiply the two square roots together, which can be simplified using the property of square roots.
Answer
$10\sqrt{3}$
Answer for screen readers
The product of the square roots is $10\sqrt{3}$.
Steps to Solve
- Write down the square roots to be multiplied
We are given two square roots to multiply: $\sqrt{30}$ and $\sqrt{10}$.
- Use the property of square roots
The property of square roots states that $\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}$. Therefore, we can rewrite the product as follows:
$$ \sqrt{30} \cdot \sqrt{10} = \sqrt{30 \cdot 10} $$
- Calculate the product inside the square root
Now we compute the product inside the square root:
$$ 30 \cdot 10 = 300 $$
So now we have:
$$ \sqrt{30} \cdot \sqrt{10} = \sqrt{300} $$
- Simplify the square root
Next, we simplify $\sqrt{300}$. We can factor $300$ into its prime factors:
$$ 300 = 100 \cdot 3 $$
Thus,
$$ \sqrt{300} = \sqrt{100 \cdot 3} = \sqrt{100} \cdot \sqrt{3} = 10\sqrt{3} $$
The product of the square roots is $10\sqrt{3}$.
More Information
The square root of 300 can be simplified using its prime factors, which makes calculations smoother. Fun fact: Square roots are often used in geometry and physics, especially in calculating distances and areas.
Tips
- A common mistake is multiplying the numbers inside the square roots incorrectly. Make sure to properly calculate the product, $30 \cdot 10 = 300$.
- Forgetting to simplify the square root can lead to an incomplete answer. Always check if the result can be simplified further.