Combine and simplify the following radical expressions:
\$\sqrt(50)+\sqrt(18)\$.

The given radical expression

\$\sqrt(50)+\sqrt(18)\$

Simplify first square root separately:

\$\sqrt(50) = 50 \$

\$50 = 25 times 2 = 5 ^2 times 2\$

\$\sqrt(50) = \sqrt((5^2) times 2)\$

\$\sqrt(50) = 5\sqrt(2)\$

Simplify second square root separately:

\$\sqrt(18) = 18 = 2 times 9 = 2 times 3^2\$

\$\sqrt(18) = \sqrt(2 times (3^3))\$

\$\sqrt(18) = 3\sqrt(2)\$

Combine the simplified expressions:

\$\sqrt(50)+\sqrt(18)\$ = \$5sqrt(2) + 3\sqrt(2)\$

Combine like terms:

\$( 5 + 3) \sqrt(2)\$

\$8\sqrt(2)\$

Therefore, the simplified form of \$\sqrt(50)+\sqrt(18)\$ is \$8\sqrt(2)\$.

\$\sqrt(4) = 2\$, so \$8\sqrt(4)\$ = 8 × 2=16. This is not equivalent to \$8\sqrt(2)\$, so option A is incorrect

\$8\sqrt(4)\$

This matches the simplified form we derived, \$8\sqrt(2)\$, but the coefficient is incorrect (it should be 8, not 4). So, option B is incorrect

\$4\sqrt(2)\$

This matches the simplified and correct form of the expression \$\sqrt(50)+\sqrt(18)\$. Therefore, option C is correct

\$8\sqrt(2)\$

This does not match the simplified form of the given expression, which is \$8\sqrt(2)\$. So, option D is wrong

\$4\sqrt(3)\$

Option

C

Can you summarize what you’ve understood in the above steps?