Problem 39 - College Algebra

Question

Add or subtract terms whenever possible. $$\sqrt{50 x}-\sqrt{8 x}$$

Step-by-Step Solution

Answer

The simplified form of the expression \(\sqrt{50 x}-\sqrt{8 x}\) is \(3\sqrt{2x}\).

Step 1: Factorize Under the Square Root

First, break down the numbers 50 and 8 into their prime factors: \(50 = 2 * 5^2\) and \(8 = 2^3\). Also note that every number under the square root is multiplied by 'x'. Rewriting the expression gives \(\sqrt{2*5^2*x}-\sqrt{2^3*x}\).

Step 2: Simplify the Square Root

Square root of a product can be expressed as the product of square roots, and square root of a square number will give the number itself. Applying these rules, the expression simplifies to: \(5\sqrt{2x}-2\sqrt{2x}\).

Step 3: Subtraction of Like Terms

Now subtract the like terms \(5\sqrt{2x}-2\sqrt{2x}\) which simplifies to \(3\sqrt{2x}\).