Basic Math Examples

$\sqrt{11 f g^{2} h^{4}} \cdot (\sqrt{40 f h^{5}})$

Step 1

Rewrite $11 f g^{2} h^{4}$ as ${(g h^{2})}^{2} \cdot (11 f)$ .

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Step 1.1

Rewrite $h^{4}$ as ${(h^{2})}^{2}$ .

$\sqrt{11 f g^{2} {(h^{2})}^{2}} \cdot \sqrt{40 f h^{5}}$

Step 1.2

Move $f$ .

$\sqrt{11 g^{2} {(h^{2})}^{2} f} \cdot \sqrt{40 f h^{5}}$

Step 1.3

Move $11$ .

$\sqrt{g^{2} {(h^{2})}^{2} \cdot 11 f} \cdot \sqrt{40 f h^{5}}$

Step 1.4

Rewrite $g^{2} {(h^{2})}^{2}$ as ${(g h^{2})}^{2}$ .

$\sqrt{{(g h^{2})}^{2} \cdot 11 f} \cdot \sqrt{40 f h^{5}}$

Step 1.5

Add parentheses.

$\sqrt{{(g h^{2})}^{2} \cdot (11 f)} \cdot \sqrt{40 f h^{5}}$

Step 2

Pull terms out from under the radical.

$g h^{2} \sqrt{11 f} \cdot \sqrt{40 f h^{5}}$

Step 3

Rewrite $40 f h^{5}$ as ${(2 h^{2})}^{2} \cdot (10 f h)$ .

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Step 3.1

Factor $4$ out of $40$ .

$g h^{2} \sqrt{11 f} \cdot \sqrt{4 (10) f h^{5}}$

Step 3.2

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

$g h^{2} \sqrt{11 f} \cdot \sqrt{2^{2} \cdot 10 f h^{5}}$

Step 3.3

Factor out $h^{4}$ .

$g h^{2} \sqrt{11 f} \cdot \sqrt{2^{2} \cdot 10 f (h^{4} h)}$

Step 3.4

Rewrite $h^{4}$ as ${(h^{2})}^{2}$ .

$g h^{2} \sqrt{11 f} \cdot \sqrt{2^{2} \cdot 10 f ({(h^{2})}^{2} h)}$

Step 3.5

Move $f$ .

$g h^{2} \sqrt{11 f} \cdot \sqrt{2^{2} \cdot 10 {(h^{2})}^{2} f h}$

Step 3.6

Move $10$ .

$g h^{2} \sqrt{11 f} \cdot \sqrt{2^{2} {(h^{2})}^{2} \cdot 10 f h}$

Step 3.7

Rewrite $2^{2} {(h^{2})}^{2}$ as ${(2 h^{2})}^{2}$ .

$g h^{2} \sqrt{11 f} \cdot \sqrt{{(2 h^{2})}^{2} \cdot 10 f h}$

Step 3.8

Add parentheses.

$g h^{2} \sqrt{11 f} \cdot \sqrt{{(2 h^{2})}^{2} \cdot 10 (f h)}$

Step 3.9

Add parentheses.

$g h^{2} \sqrt{11 f} \cdot \sqrt{{(2 h^{2})}^{2} \cdot (10 f h)}$

Step 4

Pull terms out from under the radical.

$g h^{2} \sqrt{11 f} \cdot (2 h^{2} \sqrt{10 f h})$

Step 5

Rewrite using the commutative property of multiplication.

$2 g h^{2} \sqrt{11 f} (h^{2} \sqrt{10 f h})$

Step 6

Multiply $h^{2}$ by $h^{2}$ by adding the exponents.

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Step 6.1

Move $h^{2}$ .

$2 g (h^{2} h^{2}) \sqrt{11 f} \sqrt{10 f h}$

Step 6.2

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

$2 g h^{2 + 2} \sqrt{11 f} \sqrt{10 f h}$

Step 6.3

Add $2$ and $2$ .

$2 g h^{4} \sqrt{11 f} \sqrt{10 f h}$

Step 7

Multiply $2 g h^{4} \sqrt{11 f} \sqrt{10 f h}$ .

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Step 7.1

Combine using the product rule for radicals.

$2 g h^{4} \sqrt{10 f h (11 f)}$

Step 7.2

Multiply $11$ by $10$ .

$2 g h^{4} \sqrt{110 f h f}$

Step 7.3

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

$2 g h^{4} \sqrt{110 (f^{1} f) h}$

Step 7.4

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

$2 g h^{4} \sqrt{110 (f^{1} f^{1}) h}$

Step 7.5

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

$2 g h^{4} \sqrt{110 f^{1 + 1} h}$

Step 7.6

Add $1$ and $1$ .

$2 g h^{4} \sqrt{110 f^{2} h}$

Step 8

Rewrite $110 f^{2} h$ as $f^{2} \cdot (110 h)$ .

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Step 8.1

Reorder $110$ and $f^{2}$ .

$2 g h^{4} \sqrt{f^{2} \cdot 110 h}$

Step 8.2

Add parentheses.

$2 g h^{4} \sqrt{f^{2} \cdot (110 h)}$

Step 9

Pull terms out from under the radical.

$2 g h^{4} (f \sqrt{110 h})$

Step 10

Reorder factors in $2 g h^{4} (f \sqrt{110 h})$ .

$2 g h^{4} f \sqrt{110 h}$