Simplify square root of 10st* square root of 15tu

$\sqrt{10 s t} \cdot \sqrt{15 t u}$

Step 1

Multiply $\sqrt{10 s t} \sqrt{15 t u}$ .

Combine using the product rule for radicals.

$\sqrt{10 s t (15 t u)}$

Multiply $15$ by $10$ .

$\sqrt{150 s t (t u)}$

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

$\sqrt{150 s (t^{1} t) u}$

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

$\sqrt{150 s (t^{1} t^{1}) u}$

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

$\sqrt{150 s t^{1 + 1} u}$

Add $1$ and $1$ .

$\sqrt{150 s t^{2} u}$

Step 2

Rewrite $150 s t^{2} u$ as ${(5 t)}^{2} \cdot (6 s u)$ .

Factor $25$ out of $150$ .

$\sqrt{25 (6) s t^{2} u}$

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

$\sqrt{5^{2} \cdot 6 s t^{2} u}$

Move $s$ .

$\sqrt{5^{2} \cdot 6 t^{2} s u}$

Move $6$ .

$\sqrt{5^{2} t^{2} \cdot 6 s u}$

Rewrite $5^{2} t^{2}$ as ${(5 t)}^{2}$ .

$\sqrt{{(5 t)}^{2} \cdot 6 s u}$

Add parentheses.

$\sqrt{{(5 t)}^{2} \cdot 6 (s u)}$

Add parentheses.

$\sqrt{{(5 t)}^{2} \cdot (6 s u)}$

Step 3

Pull terms out from under the radical.

$5 t \sqrt{6 s u}$