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Chapter 0: Problem 122

Explain how to add \(\sqrt{3}+\sqrt{12}\).

Short Answer

Expert verified
The sum of \(\sqrt{3}\) and \(\sqrt{12}\) is \(3*\sqrt{3}\).

Step by step solution

01

Break down the square roots

Begin by breaking down \(\sqrt{12}\). Find any perfect squares that can divide 12. By inspection, 4 is a enough perfect square that is a divisor of 12. Breaking down \(\sqrt{12}\) we get \(\sqrt{4*3}\).
02

Simplify the square roots

Now we simplify the expression. In \(\sqrt{4*3}\), the square root of 4 can be taken out, leaving us with \(2*\sqrt{3}\).
03

Add the square roots

Having simplified \(\sqrt{12}\) to \(2*\sqrt{3}\), we can now add \(\sqrt{3}\) to \(2*\sqrt{3}\). These are like terms and they sum to \(3*\sqrt{3}\).

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