What is the simplest form of the radical expression $4^{3} \sqrt{3 x} + 5^{3} \sqrt{10 x}$ $4^3sqrt(3x)+5^3sqrt(10x)$ ?

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Answer 1 · 2018-01-14T01:45:32

$\sqrt{x} [4^{3} \sqrt{3} + 5^{3} \sqrt{10}]$ $color(blue)(sqrt(x)[" "4^3sqrt(3)+5^3sqrt(10)" "]$

Given:

$4^{3} \sqrt{3 x} + 5^{3} \sqrt{10 x}$ $color(red)(4^3sqrt(3x)+5^3sqrt(10x))$

$4^{3} \sqrt{3} \sqrt{x} + 5^{3} \sqrt{10} \sqrt{x}$ $4^3sqrt(3)sqrt(x)+5^3sqrt(10)sqrt(x)$

We can see that $\sqrt{x}$ $color(blue)(sqrt(x))$ is common factor for both terms

Hence, after factoring out the common factor, we have

$\sqrt{x} [4^{3} \sqrt{3} + 5^{3} \sqrt{10}]$ $color(blue)(sqrt(x)[" "4^3sqrt(3)+5^3sqrt(10)" "]$

Hope you find this solution useful.

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