Question

1 point

Answer 1

Answer:

The simplest radical form is $9\sqrt{5}$ ⇒ (c)

Step-by-step 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 $\sqrt{8}$

factorize 8 using prime numbers

8 = 2 × 2 × 2, then $\sqrt{8}=\sqrt{(2)(2)(2)}$

Take two of 2 out the root, then $\sqrt{8}=2\sqrt{2}$

2. Simplify $\sqrt{18}$

factorize 18 using prime numbers

18 = 2 × 3 × 3, then $\sqrt{18}=\sqrt{(2)(3)(3)}$

Take the two 3 out the root, then $\sqrt{18}=3\sqrt{2}$

Let us simplify $3\sqrt{45}$

∵ 45 = 3 × 3 × 5

∴ $3\sqrt{45}=3\sqrt{(3)(3)(5)}$

→ Take the two 3 out by one 3

∴  $3\sqrt{45}=3(3)\sqrt{5}$

→ Multiply the numbers out the root

∴ $3\sqrt{45}=9\sqrt{5}$

∴ The simplest radical form is $9\sqrt{5}$