Questions: Which of the following is equivalent to (3 sqrt40-2 sqrt10) ? a.) (-sqrt30) b.) (3 sqrt30) c.) (-2 sqrt10) d.) (4 sqrt10)

Transcript text: Which of the following is equivalent to $3 \sqrt{40}-2 \sqrt{10}$ ? a.) $-\sqrt{30}$ b.) $3 \sqrt{30}$ c.) $-2 \sqrt{10}$ d.) $4 \sqrt{10}$

Solution

Solution Steps

To solve the expression $3 \sqrt{40} - 2 \sqrt{10}$, we need to simplify the square roots and combine like terms if possible. We start by simplifying $\sqrt{40}$ and then perform the arithmetic operations.

Step 1: Simplify $\sqrt{40}$

We start by simplifying $\sqrt{40}$: \[ \sqrt{40} = \sqrt{4 \times 10} = \sqrt{4} \times \sqrt{10} = 2 \sqrt{10} \]

Step 2: Substitute and Simplify the Expression

Substitute $\sqrt{40}$ with $2 \sqrt{10}$ in the original expression: \[ 3 \sqrt{40} - 2 \sqrt{10} = 3 \times 2 \sqrt{10} - 2 \sqrt{10} = 6 \sqrt{10} - 2 \sqrt{10} \]

Step 3: Combine Like Terms

Combine the like terms: \[ 6 \sqrt{10} - 2 \sqrt{10} = (6 - 2) \sqrt{10} = 4 \sqrt{10} \]