Question

Sqrt(32x^3) - sqrt(16x^3) + root(4,x^3) -sqrt(2x^3)

Answer 1

An expression is defined as a set of numbers, variables, and mathematical operations. The simplified version of the given expression is (3√2-2)√x³.

What is an Expression?

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The given expression $\sqrt{32x^3} - \sqrt{16x^3} + \sqrt{4x^3} -\sqrt{2x^3}$ can be simplified as shown below.

$\sqrt{32x^3} - \sqrt{16x^3} + \sqrt{4x^3} -\sqrt{2x^3}\\\\=\sqrt{x^3}(\sqrt{32}-\sqrt{16}+\sqrt{4}-\sqrt{2}})\\\\= \sqrt{x^3} (4\sqrt{2}-4+2-\sqrt2)\\\\= \sqrt{x^3} (3\sqrt{2}-2)$

Hence, The simplified version of the given expression is (3√2-2)√x³.

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