Question

Write the prime factorization of the radicand. Apply the product property of square roots. Write the radicand as a product, forming as many perfect square roots as possible. Simplify. What is the simplified form of 3 StartRoot 135 EndRoot? StartRoot 15 EndRoot 3 StartRoot 5 (3) EndRoot = 3 StartRoot 15 EndRoot (3 3) StartRoot 5 (3) EndRoot = 6 StartRoot 15 EndRoot 3 (3) StartRoot 5 (3) EndRoot = 9 StartRoot 15 EndRoot.

Answer 1

Answer:  $9\sqrt{15}$

Work Shown:

$x = 3\sqrt{135}\\\\x = 3\sqrt{9*15}\\\\x = 3\sqrt{9}*\sqrt{15}\\\\x = 3*3*\sqrt{15}\\\\x = 9\sqrt{15}$

In the second step, I factored 135 into 9*15 so that I could pull out the perfect square 9. This is the largest perfect square factor of 135. In the next step, I used the rule $\sqrt{A*B}=\sqrt{A}*\sqrt{B}$

Answer 2

Answer:

D- 3 (3) StartRoot 5 (3) EndRoot = 9 StartRoot 15 EndRoot