Problem 40 - College Algebra

Question

Add or subtract terms whenever possible. $$\sqrt{63 x}-\sqrt{28 x}$$

Step-by-Step Solution

Answer

\(\sqrt{7x}\)

Step 1: Factorize the Numbers

Begin by factorizing the numbers inside the square roots in the given expression. In this case, 63 can be factorized into 9*7 and 28 can be factorized into 4*7. So, now the expression can be rewritten as: \(\sqrt{9*7x} - \sqrt{4*7x}\).

Step 2: Apply Square Root Property

The square root property states that \(\sqrt{ab} = \sqrt{a}\sqrt{b}\) if a and b are positive numbers. Utilize this property to further simplify the expression. The expression hence becomes: \(3\sqrt{7x} - 2\sqrt{7x}\).

Step 3: Simplify the Final Result

Now, the expression under the square roots in both terms is the same (7x), which allows us to subtract the numeric coefficients: \(3\sqrt{7x} - 2\sqrt{7x} = (3 - 2)\sqrt{7x} = \sqrt{7x}\)