a) $$ \sqrt{6} imes \sqrt{5} imes \sqrt{10} $$

Question

a) $$ \sqrt{6} 	imes \sqrt{5} 	imes \sqrt{10} $$

UpStudy AI · Accepted Answer

To simplify the expression $$ \sqrt{6} \times \sqrt{5} \times \sqrt{10} $$, follow these steps:

1. **Combine the Square Roots:**
   
   Use the property of square roots that states $$ \sqrt{a} \times \sqrt{b} = \sqrt{a \times b} $$.

$$
   \sqrt{6} \times \sqrt{5} \times \sqrt{10} = \sqrt{6 \times 5 \times 10}
   $$

2. **Calculate the Product Inside the Square Root:**
   
   Multiply the numbers inside the square root.

$$
   6 \times 5 \times 10 = 300
   $$

So, the expression becomes:

$$
   \sqrt{300}
   $$

3. **Simplify the Square Root:**
   
   Break down 300 into its prime factors or identify a perfect square factor.

$$
   300 = 100 \times 3
   $$
   
   Since 100 is a perfect square ($$ 10^2 $$), you can simplify further:

$$
   \sqrt{300} = \sqrt{100 \times 3} = \sqrt{100} \times \sqrt{3} = 10\sqrt{3}
   $$

**Final Answer:**

$$
10\sqrt{3}
$$
The simplified form of $$ \sqrt{6} \times \sqrt{5} \times \sqrt{10} $$ is $$ 10\sqrt{3} $$.

a) \( \sqrt{6} \times \sqrt{5} \times \sqrt{10} \)