Simplify 2 square root of 2*7 square root of 18

$2 \sqrt{2} \cdot 7 \sqrt{18}$

Step 1

Rewrite $18$ as $3^{2} \cdot 2$ .

Factor $9$ out of $18$ .

$2 \sqrt{2} \cdot (7 \sqrt{9 (2)})$

Rewrite $9$ as $3^{2}$ .

$2 \sqrt{2} \cdot (7 \sqrt{3^{2} \cdot 2})$

Step 2

Pull terms out from under the radical.

$2 \sqrt{2} \cdot (7 (3 \sqrt{2}))$

Step 3

Multiply $3$ by $7$ .

$2 \sqrt{2} \cdot (21 \sqrt{2})$

Step 4

Multiply $2 \sqrt{2} (21 \sqrt{2})$ .

Multiply $21$ by $2$ .

$42 \sqrt{2} \sqrt{2}$

Raise $\sqrt{2}$ to the power of $1$ .

$42 ({\sqrt{2}}^{1} \sqrt{2})$

Raise $\sqrt{2}$ to the power of $1$ .

$42 ({\sqrt{2}}^{1} {\sqrt{2}}^{1})$

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

$42 {\sqrt{2}}^{1 + 1}$

Add $1$ and $1$ .

$42 {\sqrt{2}}^{2}$

Step 5

Rewrite ${\sqrt{2}}^{2}$ as $2$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2}$ as $2^{\frac{1}{2}}$ .

$42 {(2^{\frac{1}{2}})}^{2}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$42 \cdot 2^{\frac{1}{2} \cdot 2}$

Combine $\frac{1}{2}$ and $2$ .

$42 \cdot 2^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$42 \cdot 2^{\frac{2}{2}}$

Rewrite the expression.

$42 \cdot 2^{1}$

Evaluate the exponent.

$42 \cdot 2$

Step 6

Multiply $42$ by $2$ .

$84$