Question

Simplify the expression. $$4 \sqrt{5}+5 \sqrt{5}$$

Short answer

The simplified expression is \(9 \sqrt{5}\)

Step-by-step solution

Identify the Like Terms

The given expression is \(4 \sqrt{5}+5 \sqrt{5}\). Here both \(4 \sqrt{5}\) and \(5 \sqrt{5}\) are like terms because they both contain the \( \sqrt{5} \).

Combine Like Terms

Like terms can be combined by performing the operation between their coefficients. In the given expression, the terms \(4 \sqrt{5}\) and \(5 \sqrt{5}\) have the coefficients 4 and 5 respectively. Add these two coefficients together: \(4+5 = 9\).

Write the Simplified Expression

The simplified expression will be \(9 \sqrt{5}\), combining coefficients with the common radical.