Problem 42 - College Algebra

Question

Add or subtract terms whenever possible. $$4 \sqrt{12}-2 \sqrt{75}$$

Step-by-Step Solution

Answer

After simplification, \(4 \sqrt{12}-2 \sqrt{75} = -2 \sqrt{3}\)

Step 1: Simplify square roots

We need to simplify square roots first. This is done by finding known square numbers which are factors. For \(4 \sqrt{12}\), we realize that 12 is 4*3, so it is equivalent to \(4 \sqrt{4*3}\). Similarly, with \(2 \sqrt{75}\), we realize 75 is 25*3, so it is equivalent to \(2 \sqrt{25*3}\). Now, the given expression becomes \(4 \sqrt{4*3} - 2 \sqrt{25*3}\)

Step 2: Simplify expression

Square roots of the square numbers can be calculated. The term \(4 \sqrt{4*3}\) is equal to \(4*2 \sqrt{3} = 8 \sqrt{3}\). The term \(2 \sqrt{25*3}\) is equal to \(2*5 \sqrt{3} = 10 \sqrt{3}\). The expression now reads: \(8 \sqrt{3} - 10 \sqrt{3}\).

Step 3: Subtract

Now that we have like terms i.e., \(8 \sqrt{3}\) and \(-10 \sqrt{3}\), we can easily subtract them. Doing the subtraction, we get \(-2 \sqrt{3}\)