Simplify square root of 125x^6+10x square root of 5x^4

$\sqrt{125 x^{6}} + 10 x \sqrt{5 x^{4}}$

Step 1

Simplify each term.

Rewrite $125 x^{6}$ as ${(5 x^{3})}^{2} \cdot 5$ .

Factor $25$ out of $125$ .

$\sqrt{25 (5) x^{6}} + 10 x \sqrt{5 x^{4}}$

Rewrite $25$ as $5^{2}$ .

$\sqrt{5^{2} \cdot 5 x^{6}} + 10 x \sqrt{5 x^{4}}$

Rewrite $x^{6}$ as ${(x^{3})}^{2}$ .

$\sqrt{5^{2} \cdot 5 {(x^{3})}^{2}} + 10 x \sqrt{5 x^{4}}$

Move $5$ .

$\sqrt{5^{2} {(x^{3})}^{2} \cdot 5} + 10 x \sqrt{5 x^{4}}$

Rewrite $5^{2} {(x^{3})}^{2}$ as ${(5 x^{3})}^{2}$ .

$\sqrt{{(5 x^{3})}^{2} \cdot 5} + 10 x \sqrt{5 x^{4}}$

Pull terms out from under the radical.

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

Rewrite $5 x^{4}$ as ${(x^{2})}^{2} \cdot 5$ .

Rewrite $x^{4}$ as ${(x^{2})}^{2}$ .

$5 x^{3} \sqrt{5} + 10 x \sqrt{5 {(x^{2})}^{2}}$

Reorder $5$ and ${(x^{2})}^{2}$ .

$5 x^{3} \sqrt{5} + 10 x \sqrt{{(x^{2})}^{2} \cdot 5}$

Pull terms out from under the radical.

$5 x^{3} \sqrt{5} + 10 x (x^{2} \sqrt{5})$

Multiply $x$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

$5 x^{3} \sqrt{5} + 10 (x^{2} x) \sqrt{5}$

Multiply $x^{2}$ by $x$ .

Raise $x$ to the power of $1$ .

$5 x^{3} \sqrt{5} + 10 (x^{2} x^{1}) \sqrt{5}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$5 x^{3} \sqrt{5} + 10 x^{2 + 1} \sqrt{5}$

Add $2$ and $1$ .

$5 x^{3} \sqrt{5} + 10 x^{3} \sqrt{5}$

Step 2

Add $5 x^{3} \sqrt{5}$ and $10 x^{3} \sqrt{5}$ .

$15 x^{3} \sqrt{5}$