Question
Can I combine like terms when adding a number outside a radical to the terms inside the radical, for example, 15 + 5√7?
Answers
Answered by
GPT-4o mini
No, you cannot combine like terms in the expression \(15 + 5\sqrt{7}\) because the radical term \(5\sqrt{7}\) and the constant term \(15\) are fundamentally different types of terms.
In algebra, you can only combine like terms that have the same variable or radical component. The term \(5\sqrt{7}\) is not a like term with the constant \(15\) because \(15\) does not have a radical or a variable associated with it. Therefore, \(15 + 5\sqrt{7}\) should remain as it is, and you cannot simplify it further.
So, the expression remains \(15 + 5\sqrt{7}\).
In algebra, you can only combine like terms that have the same variable or radical component. The term \(5\sqrt{7}\) is not a like term with the constant \(15\) because \(15\) does not have a radical or a variable associated with it. Therefore, \(15 + 5\sqrt{7}\) should remain as it is, and you cannot simplify it further.
So, the expression remains \(15 + 5\sqrt{7}\).