The equivalent expressions are (a) [tex]4\sqrt 3 = \sqrt{24} \cdot \sqrt{2}[/tex], (d) [tex]4\sqrt 3 = \sqrt{12} \cdot \sqrt{4}[/tex] and (e) [tex]4\sqrt 3 = \sqrt{48}[/tex]
Equivalent expressions
Equivalent expressions are expressions that have equal values
The expression is given as:
[tex]4\sqrt 3[/tex]
Express 4 as the square root of 16
[tex]4\sqrt 3 = \sqrt{16} \times \sqrt 3[/tex]
Combine the roots
[tex]4\sqrt 3 = \sqrt{16\times 3}[/tex]
[tex]4\sqrt 3 = \sqrt{48}[/tex]
Express 48 as the product of 12 and 4
[tex]4\sqrt 3 = \sqrt{12 \cdot 4}[/tex]
Split, into factors
[tex]4\sqrt 3 = \sqrt{12} \cdot \sqrt{4}[/tex]
Express 48 as the product of 24 and 2 in [tex]4\sqrt 3 = \sqrt{48}[/tex]
[tex]4\sqrt 3 = \sqrt{24 \cdot 2}[/tex]
Split
[tex]4\sqrt 3 = \sqrt{24} \cdot \sqrt{2}[/tex]
Hence, the equivalent expressions are (a), (d) and (e)
Read more about equivalent expressions at:
https://brainly.com/question/2972832
