Given:
Number [tex]\sqrt{96}[/tex]
To find:
The simplest radical form.
Solution:
Let us first factor 96 using factor tree.
The image of the factor tree is attached below.
96 = 2 × 2 × 3 × 2 × 2 × 2
= 2² × 3 × 2 × 2²
96 = 2² × 6 × 2²
Taking square root on both sides.
[tex]\sqrt{96}=\sqrt{2^2\times 6 \times 2^2}[/tex]
[tex]\sqrt{96}=\sqrt{4\times 6 \times 4}[/tex]
[tex]\sqrt{96}=\sqrt{4^2\times 6[/tex]
Square number and square root get canceled.
[tex]\sqrt{96}=4\sqrt{ 6}[/tex]
The simplest radical form of [tex]\sqrt{96}[/tex] is [tex]4\sqrt{6}[/tex].
