Solve √5 x √20
Understand the Problem
The question asks to evaluate the product of two square roots. We can simplify this by multiplying the numbers inside the square roots and then simplifying the resulting square root.
Answer
4
Answer for screen readers
4
Steps to Solve
- Multiply the numbers inside the square roots
We can combine the two square roots into one by multiplying the numbers inside: $\sqrt{8} \cdot \sqrt{2} = \sqrt{8 \cdot 2}$
- Simplify the product inside the square root
Multiply the numbers: $\sqrt{8 \cdot 2} = \sqrt{16}$
- Evaluate the square root
Find the square root of 16: $\sqrt{16} = 4$
4
More Information
The product of $\sqrt{8}$ and $\sqrt{2}$ is 4. Note that both $\sqrt{8}$ and $\sqrt{2}$ are irrational numbers -- their decimal representations go on forever without repeating. However, their product is an integer.
Tips
A common mistake is to approximate $\sqrt{8}$ and $\sqrt{2}$ as decimals and then multiply. This will give an approximate answer, but not the exact answer. It's better to simplify using the properties of square roots first. Another common mistake is incorrectly simplifying the square root. For example, some might think that $\sqrt{16}=8$ since $8+8 = 16$. However, we are looking for a number that when multiplied by itself equals 16.
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