Questions: Add to simplify the radical expression. = 3√(2t) + 5√(48)

Solution Steps

To simplify the given radical expression, we first simplify each square root term individually. The term \( \sqrt{48} \) can be simplified by finding its prime factors and simplifying the square root. Once simplified, we combine like terms if possible.

To simplify the term \( 5 \sqrt{48} \), we first find the prime factorization of 48, which is \( 16 \times 3 \). Since \( 16 \) is a perfect square, we can simplify \( \sqrt{48} \) as follows: \[ \sqrt{48} = \sqrt{16 \times 3} = \sqrt{16} \cdot \sqrt{3} = 4\sqrt{3} \] Thus, \( 5 \sqrt{48} \) simplifies to: \[ 5 \sqrt{48} = 5 \cdot 4 \sqrt{3} = 20 \sqrt{3} \]

Now we combine the simplified term with the other term in the expression: \[ 3 \sqrt{2t} + 20 \sqrt{3} \] Since \( \sqrt{2t} \) and \( \sqrt{3} \) are not like terms, we cannot combine them further.

Final Answer