Add or subtract as indicated and simplify.
$\sqrt{12}+\sqrt{20}-\sqrt{45}$

• A. $2\sqrt3-\sqrt5$
• B. $\sqrt3-2\sqrt5$
• C. $4\sqrt3+\sqrt5$
• D. $4\sqrt5+\sqrt3$

Answer: (A)

Verified step by step guidance

1. Start by expressing each square root in terms of its prime factors to simplify them. For example, write \(\sqrt{12}\) as \(\sqrt{4 \times 3}\), \(\sqrt{20}\) as \(\sqrt{4 \times 5}\), and \(\sqrt{45}\) as \(\sqrt{9 \times 5}\).
2. Use the property of square roots that \(\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}\) to separate the factors inside each square root. This allows you to take out perfect squares from under the root.
3. Simplify each square root by taking the square root of the perfect square factors. For example, \(\sqrt{4} = 2\) and \(\sqrt{9} = 3\), so rewrite each term accordingly.
4. Rewrite the original expression using the simplified terms, which will now be a sum and difference of terms involving \(\sqrt{3}\) and \(\sqrt{5}\).
5. Combine like terms by adding or subtracting the coefficients of the square root terms that have the same radicand (the number inside the square root). This will give you the simplified expression.