Algebra Examples

$2 \sqrt{50} \cdot 3 \sqrt{8}$

Step 1

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

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Step 1.1

Factor $25$ out of $50$ .

$2 \sqrt{25 (2)} \cdot (3 \sqrt{8})$

Step 1.2

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

$2 \sqrt{5^{2} \cdot 2} \cdot (3 \sqrt{8})$

Step 2

Pull terms out from under the radical.

$2 (5 \sqrt{2}) \cdot (3 \sqrt{8})$

Step 3

Multiply $5$ by $2$ .

$10 \sqrt{2} \cdot (3 \sqrt{8})$

Step 4

Rewrite $8$ as $2^{2} \cdot 2$ .

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Step 4.1

Factor $4$ out of $8$ .

$10 \sqrt{2} \cdot (3 \sqrt{4 (2)})$

Step 4.2

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

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

Step 5

Pull terms out from under the radical.

$10 \sqrt{2} \cdot (3 (2 \sqrt{2}))$

Step 6

Multiply $2$ by $3$ .

$10 \sqrt{2} \cdot (6 \sqrt{2})$

Step 7

Multiply $10 \sqrt{2} (6 \sqrt{2})$ .

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Step 7.1

Multiply $6$ by $10$ .

$60 \sqrt{2} \sqrt{2}$

Step 7.2

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

$60 ({\sqrt{2}}^{1} \sqrt{2})$

Step 7.3

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

$60 ({\sqrt{2}}^{1} {\sqrt{2}}^{1})$

Step 7.4

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

$60 {\sqrt{2}}^{1 + 1}$

Step 7.5

Add $1$ and $1$ .

$60 {\sqrt{2}}^{2}$

Step 8

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

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Step 8.1

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

$60 {(2^{\frac{1}{2}})}^{2}$

Step 8.2

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

$60 \cdot 2^{\frac{1}{2} \cdot 2}$

Step 8.3

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

$60 \cdot 2^{\frac{2}{2}}$

Step 8.4

Cancel the common factor of $2$ .

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Step 8.4.1

Cancel the common factor.

$60 \cdot 2^{\frac{2}{2}}$

Step 8.4.2

Rewrite the expression.

$60 \cdot 2^{1}$

Step 8.5

Evaluate the exponent.

$60 \cdot 2$

Step 9

Multiply $60$ by $2$ .

$120$