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√(15)`

Work Shown:

`x = 3√(135)\\\\x = 3√(9*15)\\\\x = 3√(9)*√(15)\\\\x = 3*3*√(15)\\\\x = 9√(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
`√(A*B)=√(A)*√(B)\\\\`

Answer 2

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