Basic Math Examples

$\sqrt{75} \cdot 4 \sqrt{48}$

Step 1

Rewrite $75$ as $5^{2} \cdot 3$ .

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Step 1.1

Factor $25$ out of $75$ .

$\sqrt{25 (3)} \cdot (4 \sqrt{48})$

Step 1.2

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

$\sqrt{5^{2} \cdot 3} \cdot (4 \sqrt{48})$

Step 2

Pull terms out from under the radical.

$5 \sqrt{3} \cdot (4 \sqrt{48})$

Step 3

Rewrite $48$ as $4^{2} \cdot 3$ .

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Step 3.1

Factor $16$ out of $48$ .

$5 \sqrt{3} \cdot (4 \sqrt{16 (3)})$

Step 3.2

Rewrite $16$ as $4^{2}$ .

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

Step 4

Pull terms out from under the radical.

$5 \sqrt{3} \cdot (4 (4 \sqrt{3}))$

Step 5

Multiply $4$ by $4$ .

$5 \sqrt{3} \cdot (16 \sqrt{3})$

Step 6

Multiply $5 \sqrt{3} (16 \sqrt{3})$ .

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Step 6.1

Multiply $16$ by $5$ .

$80 \sqrt{3} \sqrt{3}$

Step 6.2

Raise $\sqrt{3}$ to the power of $1$ .

$80 ({\sqrt{3}}^{1} \sqrt{3})$

Step 6.3

Raise $\sqrt{3}$ to the power of $1$ .

$80 ({\sqrt{3}}^{1} {\sqrt{3}}^{1})$

Step 6.4

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

$80 {\sqrt{3}}^{1 + 1}$

Step 6.5

Add $1$ and $1$ .

$80 {\sqrt{3}}^{2}$

Step 7

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

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Step 7.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$80 {(3^{\frac{1}{2}})}^{2}$

Step 7.2

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

$80 \cdot 3^{\frac{1}{2} \cdot 2}$

Step 7.3

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

$80 \cdot 3^{\frac{2}{2}}$

Step 7.4

Cancel the common factor of $2$ .

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Step 7.4.1

Cancel the common factor.

$80 \cdot 3^{\frac{2}{2}}$

Step 7.4.2

Rewrite the expression.

$80 \cdot 3^{1}$

Step 7.5

Evaluate the exponent.

$80 \cdot 3$

Step 8

Multiply $80$ by $3$ .

$240$