Simplify The Expression:$\sqrt{2} \cdot \sqrt{10}$

**Simplify the Expression: $\sqrt{2} \cdot \sqrt{10}$** =====================================================

What is the Simplified Form of $\sqrt{2} \cdot \sqrt{10}$?

The expression $\sqrt{2} \cdot \sqrt{10}$ can be simplified using the properties of radicals. When we multiply two square roots, we can combine them into a single square root by multiplying the numbers inside the radicals.

How to Simplify $\sqrt{2} \cdot \sqrt{10}$?

To simplify the expression $\sqrt{2} \cdot \sqrt{10}$, we can use the property of radicals that states $\sqrt{a} \cdot \sqrt{b} = \sqrt{ab}$. In this case, we have:

$$\sqrt{2} \cdot \sqrt{10} = \sqrt{2 \cdot 10}$$

What is the Value of $\sqrt{2 \cdot 10}$?

Now, we can simplify the expression inside the radical by multiplying 2 and 10:

$$\sqrt{2 \cdot 10} = \sqrt{20}$$

Can We Simplify $\sqrt{20}$ Further?

Yes, we can simplify $\sqrt{20}$ further by factoring 20 into its prime factors:

$$20 = 2 \cdot 2 \cdot 5$$

How Does This Help Us Simplify $\sqrt{20}$?

Now that we have factored 20 into its prime factors, we can rewrite $\sqrt{20}$ as:

$$\sqrt{20} = \sqrt{2 \cdot 2 \cdot 5}$$

What is the Simplified Form of $\sqrt{2 \cdot 2 \cdot 5}$?

Using the property of radicals that states $\sqrt{a} \cdot \sqrt{b} = \sqrt{ab}$, we can rewrite $\sqrt{2 \cdot 2 \cdot 5}$ as:

$$\sqrt{2 \cdot 2 \cdot 5} = \sqrt{(2 \cdot 2) \cdot 5}$$

Can We Simplify $\sqrt{(2 \cdot 2) \cdot 5}$ Further?

Yes, we can simplify $\sqrt{(2 \cdot 2) \cdot 5}$ further by evaluating the expression inside the radical:

$$\sqrt{(2 \cdot 2) \cdot 5} = \sqrt{4 \cdot 5}$$

What is the Simplified Form of $\sqrt{4 \cdot 5}$?

Using the property of radicals that states $\sqrt{a} \cdot \sqrt{b} = \sqrt{ab}$, we can rewrite $\sqrt{4 \cdot 5}$ as:

$$\sqrt{4 \cdot 5} = \sqrt{4} \cdot \sqrt{5}$$

What is the Value of $\sqrt{4} \cdot \sqrt{5}$?

Now, we can evaluate the expression $\sqrt{4} \cdot \sqrt{5}$:

$$\sqrt{4} \cdot \sqrt{5} = 2 \cdot \sqrt{5}$$

What is the Final Simplified Form of $\sqrt{2} \cdot \sqrt{10}$?

Therefore, the final simplified form of $\sqrt{2} \cdot \sqrt{10}$ is:

$$\sqrt{2} \cdot \sqrt{10} = 2\sqrt{5}$$

Conclusion

In this article, we have simplified the expression $\sqrt{2} \cdot \sqrt{10}$ using the properties of radicals. We have shown that the simplified form of $\sqrt{2} \cdot \sqrt{10}$ is $2\sqrt{5}$. This result can be used to simplify more complex expressions involving radicals.

Frequently Asked Questions

Q: What is the simplified form of $\sqrt{2} \cdot \sqrt{10}$?

A: The simplified form of $\sqrt{2} \cdot \sqrt{10}$ is $2\sqrt{5}$.

Q: How do I simplify $\sqrt{2} \cdot \sqrt{10}$?

A: To simplify $\sqrt{2} \cdot \sqrt{10}$, you can use the property of radicals that states $\sqrt{a} \cdot \sqrt{b} = \sqrt{ab}$.

Q: Can I simplify $\sqrt{20}$ further?

A: Yes, you can simplify $\sqrt{20}$ further by factoring 20 into its prime factors.

Q: What is the value of $\sqrt{4} \cdot \sqrt{5}$?

A: The value of $\sqrt{4} \cdot \sqrt{5}$ is $2 \cdot \sqrt{5}$.

Q: What is the final simplified form of $\sqrt{2} \cdot \sqrt{10}$?

A: The final simplified form of $\sqrt{2} \cdot \sqrt{10}$ is $2\sqrt{5}$.