Question

simplify the radical expression.

1. $(3sqrt{14})(sqrt{35})$

Explanation:

Step1: Multiply coefficients and radicands

$3 \times \sqrt{14 \times 35}$

Step2: Factor radicand into primes

$3 \times \sqrt{2 \times 7 \times 5 \times 7}$

Step3: Group perfect square factors

$3 \times \sqrt{7^2 \times 2 \times 5}$

Step4: Simplify perfect square radical

$3 \times 7 \times \sqrt{10}$

Step5: Multiply remaining coefficients

$21 \times \sqrt{10}$

Answer:

$21\sqrt{10}$