Is the simplified form of 2square root of 3 ⋅ 2square root of 6 rational
Yes or No
I did the Homework and the lesson so the answer is No
2 sqrt 3 * 2 sqrt (2*3)
= 4 sqrt (9*2)
= 12 sqrt 2
sqrt 2 is NOT rational
Yes, the simplified form of 2√3 ⋅ 2√6 is rational.
To determine whether the simplified form of 2√3 ⋅ 2√6 is rational or not, we need to simplify the expression first.
Let's start by simplifying the square roots separately:
√3 cannot be simplified any further because 3 is not a perfect square.
Now, let's simplify √6. We can rewrite 6 as the product of two perfect squares: 2 ⋅ 3.
√6 = √(2 ⋅ 3) = √2 ⋅ √3.
Now, substitute the simplified forms back into the original expression:
2√3 ⋅ 2√6 = 2√3 ⋅ 2(√2 ⋅ √3).
By using the associative property, we can rearrange the expression:
= 2⋅2 ⋅ √3 ⋅ (√2 ⋅ √ 3).
Now, simplify the numerical part:
= 4 ⋅ 3 ⋅ √2.
= 12√2.
Since 12√2 is in the form of a constant multiplied by a square root, and there are no square roots in the denominator, we can conclude that the simplified form, 12√2, is irrational.
Therefore, the answer to your question is No - the simplified form of 2√3 ⋅ 2√6 is not rational.