Is the simplified form of 2 square root of 3 ⋅ 2 square root of 6 rational?
yes or no i think its yes pls help
(2√3)(2√6)
= 6√18
= 6√9 √2
= 18√2 , still irrational
are you guessing?
What makes you think this one, and the last one, is rational
To determine if the simplified form of 2√3 ⋅ 2√6 is rational or not, let's simplify the expression first.
We can combine these square roots by multiplying the coefficients (numbers outside the square root) and simplifying the value inside the square root:
2√3 ⋅ 2√6 = 2 * 2 * √(3 * 6) = 4√(18).
Now, let's simplify the square root of 18. We can factor out the largest square number from 18, which is 9:
4√(18) = 4 * √(9 * 2) = 4 * √9 * √2 = 4 * 3 * √2 = 12√2.
Now we have the simplified expression 12√2.
To determine if this is rational or not, we need to check if the expression can be written as a fraction of two integers. If it can be written in this form, it is rational. Otherwise, it is irrational.
In the case of 12√2, the expression cannot be simplified further as an integer fraction and therefore cannot be written as a rational number. So the answer is no, the simplified form of 2√3 ⋅ 2√6 is not rational.