The expression equivalent to [tex]5x\sqrt{28x^{5} } + 8x^{3} \sqrt{7x}[/tex] is [tex]18x^{3}\sqrt{7x}[/tex].
Simplification
What is simplification?
In order to simplify an expression, multiple processes must be used to reduce it to a simpler form.
Formula used in simplification:
[tex]\sqrt[n]{ab} =\sqrt[n]{a} .\sqrt[n]{b}[/tex]
Simplification of given expression:
= [tex]5x\sqrt{28x^{5} } + 8x^{3} \sqrt{7x}[/tex]
= [tex]5x\sqrt{4*7x^{5} } + 8x^{3} \sqrt{7x}[/tex]
= [tex]5x\sqrt{2^{2} *7x^{4}x } + 8x^{3} \sqrt{7x}[/tex]
Apply the simplification formula
= [tex]5x\sqrt{2^{2}} \sqrt{x^{4} } \sqrt{7x} + 8x^{3} \sqrt{7x}[/tex]
= [tex]5x*2x^{2} \sqrt{7x} + 8x^{3} \sqrt{7x}[/tex]
Further solve,
= [tex]10x^{3} \sqrt{7x} + 8x^{3} \sqrt{7x}[/tex]
= [tex]18x^{3} \sqrt{7x}[/tex]
The expression equivalent to [tex]5x\sqrt{28x^{5} } + 8x^{3} \sqrt{7x}[/tex] is [tex]18x^{3}\sqrt{7x}[/tex].
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