Simplify square root of 50*3 square root of 2

$\sqrt{50} \cdot 3 \sqrt{2}$

Step 1

Rewrite $50$ as $5^{2} \cdot 2$ .

Factor $25$ out of $50$ .

$\sqrt{25 (2)} \cdot (3 \sqrt{2})$

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

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

Step 2

Pull terms out from under the radical.

$5 \sqrt{2} \cdot (3 \sqrt{2})$

Step 3

Multiply $5 \sqrt{2} (3 \sqrt{2})$ .

Multiply $3$ by $5$ .

$15 \sqrt{2} \sqrt{2}$

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

$15 ({\sqrt{2}}^{1} \sqrt{2})$

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

$15 ({\sqrt{2}}^{1} {\sqrt{2}}^{1})$

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

$15 {\sqrt{2}}^{1 + 1}$

Add $1$ and $1$ .

$15 {\sqrt{2}}^{2}$

Step 4

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

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

$15 {(2^{\frac{1}{2}})}^{2}$

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

$15 \cdot 2^{\frac{1}{2} \cdot 2}$

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

$15 \cdot 2^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$15 \cdot 2^{\frac{2}{2}}$

Rewrite the expression.

$15 \cdot 2^{1}$

Evaluate the exponent.

$15 \cdot 2$

Step 5

Multiply $15$ by $2$ .

$30$