Simplify √5 x √20
Understand the Problem
The question requires simplifying the given expression involving square roots. We can simplify this by multiplying the numbers inside the square roots and then simplifying the resulting square root, if necessary.
Answer
$3\sqrt{10}$
Answer for screen readers
$3\sqrt{10}$
Steps to Solve
- Multiply the numbers inside the square roots
To simplify the expression $\sqrt{6} \cdot \sqrt{15}$, we first multiply the numbers inside the square roots: $\sqrt{6 \cdot 15} = \sqrt{90}$
- Find the prime factorization of the result
Now we find the prime factorization of 90: $90 = 2 \cdot 45 = 2 \cdot 3 \cdot 15 = 2 \cdot 3 \cdot 3 \cdot 5 = 2 \cdot 3^2 \cdot 5$
- Simplify the square root
We can rewrite the square root as: $\sqrt{90} = \sqrt{2 \cdot 3^2 \cdot 5} = \sqrt{3^2} \cdot \sqrt{2 \cdot 5} = 3 \sqrt{10}$
$3\sqrt{10}$
More Information
The simplified form of $\sqrt{6} \cdot \sqrt{15}$ is $3\sqrt{10}$, which is an irrational number.
Tips
A common mistake is not fully simplifying the square root. For example, stopping at $\sqrt{90}$ is not the simplest form. Always look for perfect square factors within the square root.
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