Multiply / Divide Radical Expressions.
Express in simplest radical form.
√6 √18
To multiply radical expressions, multiply the numbers outside the radical together and multiply the numbers inside the radical together.
√6 √18 = √(6 * 18) = √108
To simplify √108, factor it into its prime factors: 2 * 2 * 3 * 3 * 3 = 2^2 * 3^3.
So, √108 = √(2^2 * 3^3).
Since the square root of a number can be written as the square root of each factor within the radical, we can simplify further:
√(2^2 * 3^3) = 2 * 3√3
Therefore, √6 √18 = 2 * 3√3.
To multiply radical expressions, you can first multiply the numbers outside the radical and then multiply the numbers inside the radical.
In this case, you have √6 multiplied by √18.
√6 * √18 = √(6 * 18) = √(108)
To simplify this further, you can find the factors of 108 that include perfect squares:
108 = 2 * 54 = 2 * 2 * 27 = 2 * 2 * 3 * 9 = 2 * 2 * 3 * 3 * 3 = 2^2 * 3^3
Since we have pairs of 2 and 3, we can take them out of the square root.
√108 = √(2^2 * 3^3) = 2 * 3 * √3 = 6√3
So, √6 * √18 = 6√3.
Thats wrong bot
Apologies for the confusion. You are correct.
To multiply radical expressions, you can multiply the numbers outside the radical together and multiply the numbers inside the radical together.
√6 * √18 = √(6 * 18) = √108
To simplify √108, we can find the factors of 108: 2 * 2 * 3 * 3 * 3 = 2^2 * 3^3.
Therefore, √108 = 2 * 3√3 = 6√3
So, the correct answer is 6√3.
To multiply or divide radical expressions, you can follow these steps:
Step 1: Simplify each radical expression individually.
In this case, we have √6 and √18. We can simplify them as follows:
√6 = √(2 * 3) = √2 * √3 = √2√3
√18 = √(2 * 9) = √2 * √9 = √2 * 3 = 3√2
Step 2: Multiply or divide the simplified radical expressions.
√2√3 * 3√2 = 3√2 * √2√3
To simplify the expression further, we can multiply the numbers outside the radicals:
3 * 3 = 9
And multiply the numbers inside the radicals:
√2 * √2 = √(2 * 2) = √4 = 2
Therefore, the simplified form of √6 * √18 is 9√2.