Question

use the product rule to simplify the radical.
$7\sqrt{90}$

$7\sqrt{90} = \square$
(simplify your answer. type an exact answer, using radicals as needed.)

Explanation:

Step1: Factor 90 into perfect square

$90 = 9 \times 10$

Step2: Apply product rule for radicals

$7\sqrt{90} = 7\sqrt{9 \times 10} = 7 \times \sqrt{9} \times \sqrt{10}$

Step3: Simplify $\sqrt{9}$

$\sqrt{9} = 3$, so $7 \times 3 \times \sqrt{10}$

Step4: Multiply coefficients

$7 \times 3 = 21$

Answer:

$21\sqrt{10}$