Is the simplified form of 2square root of 3 + 3square root of 3 rational?
\(2\sqrt3+3\sqrt3=(2+3)\sqrt3=\boxed{5\sqrt3}\in\mathbb{R}\\\\It's\ not\ rational.\)
Answer:
No, the simplified form is not rational.
Step-by-step explanation:
We have been given the expression \(2\sqrt3+3\sqrt3\)
We can easily simplify this expression by adding the terms. We can add the terms because both have the same radical.
On adding, we get
\(2\sqrt3+3\sqrt3=5\sqrt3\)
Now, we know that \(\sqrt3\) is an irrational number. Now, we know that the product of rational and irrational is irrational . Hence, when we multiply a rational number 5 with irrational number \(\sqrt3\) then the result would be irrational.
Hence, the simplified form is irrational