Question

1 point

What is 3V45 expressed in simplest radical form?
a. 615
b. 2715
c. 9/5
d. 515
b
Ο Ο Ο Ο
d

Answer 1

The simplest radical form is
`9√(5)` ⇒ (c)

Explanation:

To simplify any square root;

• Factorize the number under the root using prime numbers

• Take out the root any number repeated twice as one number

Examples:

1. Simplify
`√(8)`

factorize 8 using prime numbers

8 = 2 × 2 × 2, then
`√(8)=√((2)(2)(2))`

Take two of 2 out the root, then
`√(8)=2√(2)`

2. Simplify
`√(18)`

factorize 18 using prime numbers

18 = 2 × 3 × 3, then
`√(18)=√((2)(3)(3))`

Take the two 3 out the root, then
`√(18)=3√(2)`

Let us simplify
`3√(45)`

∵ 45 = 3 × 3 × 5

∴
`3√(45)=3√((3)(3)(5))`

→ Take the two 3 out by one 3

∴
`3√(45)=3(3)√(5)`

→ Multiply the numbers out the root

∴
`3√(45)=9√(5)`

∴ The simplest radical form is
`9√(5)`