Step 1a

Simplify inside the square roots:

\$ \sqrt (36v^2) = 6v \$(since \$ \sqrt(36) = 6 \$)

\$ \sqrt(100uv) = 10\sqrt(uv) \$

So the expression becomes:

\$ 3u 6v \div 12(10\sqrt(uv)) \$

Explanation: We simplified the expressions inside the square roots and then substituted these simplified forms into the given expression.

Step 1b

Simplify the constants:

\$ 3 \times 6 = 18 \$

\$ 12 \times 10 = 120 \$

Substitute these values:

\$ 18uv \div 120(\sqrt(100uv)) \$

Explanation: We simplified the numbers and then used these simplified values in the expression.

Step 1c

Simplify the fraction (reduce the fraction):

Simplify \$ 18uv \div 120(\sqrt(100uv)) \$

Divide both numerator and denominator by 6:

\$ 3uv \div 20\sqrt(uv) \$

Therefore, the simplified expression is \$ 3uv \div 20\sqrt(uv) \$.

Explanation: After reducing the fraction, we determine the final result.