What is the following product: sqrt(12) * sqrt(18)?
Understand the Problem
The question is asking us to find the product of the square roots of 12 and 18. To solve this, we can first calculate the square roots individually and then multiply the results together.
Answer
$6\sqrt{6}$
Answer for screen readers
The product of the square roots of 12 and 18 is $6\sqrt{6}$.
Steps to Solve
- Calculate the square root of 12
To find the square root of 12, we can break it down into its prime factors. The prime factorization of 12 is $12 = 4 \times 3 = 2^2 \times 3$.
So, $$ \sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3} $$
- Calculate the square root of 18
Next, we perform the same process for 18. The prime factorization of 18 is $18 = 9 \times 2 = 3^2 \times 2$.
So, $$ \sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \times \sqrt{2} = 3\sqrt{2} $$
- Multiply the results together
Now, we can multiply the two square roots we just calculated: $$ \sqrt{12} \times \sqrt{18} = (2\sqrt{3}) \times (3\sqrt{2}) $$
To do this multiplication, we will multiply the coefficients and the square roots separately: $$ (2 \times 3) \times (\sqrt{3} \times \sqrt{2}) = 6 \times \sqrt{6} $$
The product of the square roots of 12 and 18 is $6\sqrt{6}$.
More Information
The result $6\sqrt{6}$ combines the coefficients and the square roots into a single expression. This is a simplified form and represents the multiplication of the two square roots effectively.
Tips
- Forgetting to simplify the square roots when possible.
- Confusing the multiplication process of square roots; remember to multiply coefficients and the square roots separately.
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