Simplify 7 square root of 5x^3*9x square root of 24x

$7 \sqrt{5 x^{3}} \cdot 9 x \sqrt{24 x}$

Step 1

Rewrite $5 x^{3}$ as $x^{2} \cdot (5 x)$ .

Factor out $x^{2}$ .

$7 \sqrt{5 (x^{2} x)} \cdot (9 x \sqrt{24 x})$

Reorder $5$ and $x^{2}$ .

$7 \sqrt{x^{2} \cdot 5 x} \cdot (9 x \sqrt{24 x})$

Add parentheses.

$7 \sqrt{x^{2} \cdot (5 x)} \cdot (9 x \sqrt{24 x})$

Step 2

Pull terms out from under the radical.

$7 (x \sqrt{5 x}) \cdot (9 x \sqrt{24 x})$

Step 3

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$7 (x \cdot x \sqrt{5 x}) \cdot (9 \sqrt{24 x})$

Multiply $x$ by $x$ .

$7 (x^{2} \sqrt{5 x}) \cdot (9 \sqrt{24 x})$

Step 4

Rewrite $24 x$ as $2^{2} \cdot (6 x)$ .

Factor $4$ out of $24$ .

$7 x^{2} \sqrt{5 x} \cdot (9 \sqrt{4 (6) x})$

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

$7 x^{2} \sqrt{5 x} \cdot (9 \sqrt{2^{2} \cdot 6 x})$

Add parentheses.

$7 x^{2} \sqrt{5 x} \cdot (9 \sqrt{2^{2} \cdot (6 x)})$

Step 5

Pull terms out from under the radical.

$7 x^{2} \sqrt{5 x} \cdot (9 (2 \sqrt{6 x}))$

Step 6

Multiply $2$ by $9$ .

$7 x^{2} \sqrt{5 x} \cdot (18 \sqrt{6 x})$

Step 7

Multiply $7 x^{2} \sqrt{5 x} (18 \sqrt{6 x})$ .

Multiply $18$ by $7$ .

$126 x^{2} \sqrt{5 x} \sqrt{6 x}$

Combine using the product rule for radicals.

$126 x^{2} \sqrt{6 x (5 x)}$

Multiply $5$ by $6$ .

$126 x^{2} \sqrt{30 x \cdot x}$

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

$126 x^{2} \sqrt{30 (x^{1} x)}$

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

$126 x^{2} \sqrt{30 (x^{1} x^{1})}$

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

$126 x^{2} \sqrt{30 x^{1 + 1}}$

Add $1$ and $1$ .

$126 x^{2} \sqrt{30 x^{2}}$

Step 8

Reorder $30$ and $x^{2}$ .

$126 x^{2} \sqrt{x^{2} \cdot 30}$

Step 9

Pull terms out from under the radical.

$126 x^{2} (x \sqrt{30})$

Step 10

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

Move $x$ .

$126 (x \cdot x^{2}) \sqrt{30}$

Multiply $x$ by $x^{2}$ .

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

$126 (x^{1} x^{2}) \sqrt{30}$

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

$126 x^{1 + 2} \sqrt{30}$

Add $1$ and $2$ .

$126 x^{3} \sqrt{30}$

Simplify 7 square root of 5x^3*9x square root of 24x

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