Step 1a

Multiply the coefficients (numbers outside the radicals): \$2 times 3 times 7 = 42\$

Multiply the radicals using the property: \$\sqrt(a) times \sqrt(b) = \sqrt(a. b)\$

\$\sqrt(5) times \sqrt(10) times \sqrt(45) = \sqrt(5 . 10. 45)\$

Simplify the expression inside the radical: \$5. 10. (9.5) = 25. 90 = 2250\$.

Explanation: Multiply the coefficients, then the radicals using their properties, and finally simplify the inside the radical.

Step 1b

Simplify the radical: \$\sqrt(2250)\$

Factor 2250 to find perfect squares: \$2. 3^2. 5^3 \$

\$\sqrt(2250) = \sqrt(2. 5. 3^2. 5^2) = 3. 5\sqrt(2.5) = 15\sqrt(10)\$

Combine the coefficient with the simplified radical: \$42. 15 \sqrt(10) = 630\sqrt(10)\$

Therefore, the simplified expression is \$630\sqrt(10)\$.

Explanation: Factor out the 2250, combine the coefficient with the simplified radicals, and then find the final result.