Finite Math Examples

$\sqrt{10 x z^{10}} (\sqrt{30 x^{17} z})$

Step 1

Rewrite $10 x z^{10}$ as ${(z^{5})}^{2} \cdot (10 x)$ .

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Step 1.1

Rewrite $z^{10}$ as ${(z^{5})}^{2}$ .

$\sqrt{10 x {(z^{5})}^{2}} \sqrt{30 x^{17} z}$

Step 1.2

Move $x$ .

$\sqrt{10 {(z^{5})}^{2} x} \sqrt{30 x^{17} z}$

Step 1.3

Reorder $10$ and ${(z^{5})}^{2}$ .

$\sqrt{{(z^{5})}^{2} \cdot 10 x} \sqrt{30 x^{17} z}$

Step 1.4

Add parentheses.

$\sqrt{{(z^{5})}^{2} \cdot (10 x)} \sqrt{30 x^{17} z}$

Step 2

Pull terms out from under the radical.

$z^{5} \sqrt{10 x} \sqrt{30 x^{17} z}$

Step 3

Rewrite $30 x^{17} z$ as ${({(x^{4})}^{2})}^{2} \cdot (30 x z)$ .

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Step 3.1

Factor out $x^{16}$ .

$z^{5} \sqrt{10 x} \sqrt{30 (x^{16} x) z}$

Step 3.2

Rewrite $x^{16}$ as ${(x^{8})}^{2}$ .

$z^{5} \sqrt{10 x} \sqrt{30 ({(x^{8})}^{2} x) z}$

Step 3.3

Reorder $30$ and ${(x^{8})}^{2}$ .

$z^{5} \sqrt{10 x} \sqrt{{(x^{8})}^{2} \cdot 30 x z}$

Step 3.4

Rewrite $x^{8}$ as ${(x^{4})}^{2}$ .

$z^{5} \sqrt{10 x} \sqrt{{({(x^{4})}^{2})}^{2} \cdot 30 x z}$

Step 3.5

Add parentheses.

$z^{5} \sqrt{10 x} \sqrt{{({(x^{4})}^{2})}^{2} \cdot 30 (x z)}$

Step 3.6

Add parentheses.

$z^{5} \sqrt{10 x} \sqrt{{({(x^{4})}^{2})}^{2} \cdot (30 x z)}$

Step 4

Pull terms out from under the radical.

$z^{5} \sqrt{10 x} ({(x^{4})}^{2} \sqrt{30 x z})$

Step 5

Multiply the exponents in ${(x^{4})}^{2}$ .

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Step 5.1

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

$z^{5} \sqrt{10 x} (x^{4 \cdot 2} \sqrt{30 x z})$

Step 5.2

Multiply $4$ by $2$ .

$z^{5} \sqrt{10 x} (x^{8} \sqrt{30 x z})$

Step 6

Multiply $z^{5} \sqrt{10 x} (x^{8} \sqrt{30 x z})$ .

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Step 6.1

Combine using the product rule for radicals.

$z^{5} (x^{8} \sqrt{10 x (30 x z)})$

Step 6.2

Multiply $30$ by $10$ .

$z^{5} (x^{8} \sqrt{300 x (x z)})$

Step 6.3

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

$z^{5} (x^{8} \sqrt{300 (x^{1} x) z})$

Step 6.4

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

$z^{5} (x^{8} \sqrt{300 (x^{1} x^{1}) z})$

Step 6.5

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

$z^{5} (x^{8} \sqrt{300 x^{1 + 1} z})$

Step 6.6

Add $1$ and $1$ .

$z^{5} (x^{8} \sqrt{300 x^{2} z})$

Step 7

Rewrite $300 x^{2} z$ as ${(10 x)}^{2} \cdot (3 z)$ .

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Step 7.1

Factor $100$ out of $300$ .

$z^{5} (x^{8} \sqrt{100 (3) x^{2} z})$

Step 7.2

Rewrite $100$ as $10^{2}$ .

$z^{5} (x^{8} \sqrt{10^{2} \cdot 3 x^{2} z})$

Step 7.3

Move $3$ .

$z^{5} (x^{8} \sqrt{10^{2} x^{2} \cdot 3 z})$

Step 7.4

Rewrite $10^{2} x^{2}$ as ${(10 x)}^{2}$ .

$z^{5} (x^{8} \sqrt{{(10 x)}^{2} \cdot 3 z})$

Step 7.5

Add parentheses.

$z^{5} (x^{8} \sqrt{{(10 x)}^{2} \cdot (3 z)})$

Step 8

Pull terms out from under the radical.

$z^{5} (x^{8} (10 x \sqrt{3 z}))$

Step 9

Rewrite using the commutative property of multiplication.

$10 z^{5} (x^{8} x \sqrt{3 z})$

Step 10

Multiply $x^{8}$ by $x$ by adding the exponents.

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Step 10.1

Multiply $x^{8}$ by $x$ .

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Step 10.1.1

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

$10 z^{5} (x^{8} x^{1} \sqrt{3 z})$

Step 10.1.2

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

$10 z^{5} (x^{8 + 1} \sqrt{3 z})$

Step 10.2

Add $8$ and $1$ .

$10 z^{5} (x^{9} \sqrt{3 z})$

$10 z^{5} x^{9} \sqrt{3 z}$