Simplify square root of x^3+1

$\sqrt{x^{3} + 1}$

Step 1

Rewrite $1$ as $1^{3}$ .

$\sqrt{x^{3} + 1^{3}}$

Step 2

Since both terms are perfect cubes, factor using the sum of cubes formula, $a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2})$ where $a = x$ and $b = 1$ .

$\sqrt{(x + 1) (x^{2} - x \cdot 1 + 1^{2})}$

Step 3

Simplify.

Multiply $- 1$ by $1$ .

$\sqrt{(x + 1) (x^{2} - x + 1^{2})}$

One to any power is one.

$\sqrt{(x + 1) (x^{2} - x + 1)}$

Simplify square root of x^3+1

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