simplify radical expression
Check the final answer first, then review the worked steps.
Problem
simplify radical expression
Answer
\(21\sqrt{2}\)
Step-by-step solution
- Identify the expression: The problem asks to simplify the expression $7\sqrt{18}$.
- Factor the radicand: To simplify the square root, we look for perfect square factors of $18$. We know that $18 = 9 \times 2$, and $9$ is a perfect square ($3^2$).
- Apply the product property of radicals: Using the property $\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}$, we can rewrite the expression as: $$7\sqrt{9 \cdot 2} = 7 \cdot \sqrt{9} \cdot \sqrt{2}$$
- Simplify the square root: Since $\sqrt{9} = 3$, substitute this back into the expression: $$7 \cdot 3 \cdot \sqrt{2}$$
- Multiply the constants: Multiply the coefficients $7$ and $3$: $$21\sqrt{2}$$