Simplify square root of 2x( square root of 10x+6 square root of x)

$\sqrt{2 x} (\sqrt{10 x} + 6 \sqrt{x})$

Step 1

Apply the distributive property.

$\sqrt{2 x} \sqrt{10 x} + \sqrt{2 x} (6 \sqrt{x})$

Step 2

Multiply $\sqrt{2 x} \sqrt{10 x}$ .

Combine using the product rule for radicals.

$\sqrt{2 x (10 x)} + \sqrt{2 x} (6 \sqrt{x})$

Multiply $10$ by $2$ .

$\sqrt{20 x \cdot x} + \sqrt{2 x} (6 \sqrt{x})$

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

$\sqrt{20 (x^{1} x)} + \sqrt{2 x} (6 \sqrt{x})$

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

$\sqrt{20 (x^{1} x^{1})} + \sqrt{2 x} (6 \sqrt{x})$

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

$\sqrt{20 x^{1 + 1}} + \sqrt{2 x} (6 \sqrt{x})$

Add $1$ and $1$ .

$\sqrt{20 x^{2}} + \sqrt{2 x} (6 \sqrt{x})$

Step 3

Rewrite using the commutative property of multiplication.

$\sqrt{20 x^{2}} + 6 \sqrt{2 x} \sqrt{x}$

Step 4

Simplify each term.

Rewrite $20 x^{2}$ as ${(2 x)}^{2} \cdot 5$ .

Factor $4$ out of $20$ .

$\sqrt{4 (5) x^{2}} + 6 \sqrt{2 x} \sqrt{x}$

Rewrite $4$ as $2^{2}$ .

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

Move $5$ .

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

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

$\sqrt{{(2 x)}^{2} \cdot 5} + 6 \sqrt{2 x} \sqrt{x}$

Pull terms out from under the radical.

$2 x \sqrt{5} + 6 \sqrt{2 x} \sqrt{x}$

Multiply $6 \sqrt{2 x} \sqrt{x}$ .

Combine using the product rule for radicals.

$2 x \sqrt{5} + 6 \sqrt{x (2 x)}$

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

$2 x \sqrt{5} + 6 \sqrt{2 (x^{1} x)}$

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

$2 x \sqrt{5} + 6 \sqrt{2 (x^{1} x^{1})}$

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

$2 x \sqrt{5} + 6 \sqrt{2 x^{1 + 1}}$

Add $1$ and $1$ .

$2 x \sqrt{5} + 6 \sqrt{2 x^{2}}$

Reorder $2$ and $x^{2}$ .

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

Pull terms out from under the radical.

$2 x \sqrt{5} + 6 x \sqrt{2}$

Simplify square root of 2x( square root of 10x+6 square root of x)

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