Simplify square root of 3x^4* square root of 5x^2* square root of 10

$\sqrt{3 x^{4}} \cdot \sqrt{5 x^{2}} \cdot \sqrt{10}$

Step 1

Rewrite $3 x^{4}$ as ${(x^{2})}^{2} \cdot 3$ .

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

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

Reorder $3$ and ${(x^{2})}^{2}$ .

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

Step 2

Pull terms out from under the radical.

$x^{2} \sqrt{3} \cdot \sqrt{5 x^{2}} \cdot \sqrt{10}$

Step 3

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

$x^{2} \sqrt{3} \cdot \sqrt{x^{2} \cdot 5} \cdot \sqrt{10}$

Step 4

Pull terms out from under the radical.

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

Step 5

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

Move $x$ .

$x \cdot x^{2} \sqrt{3} \cdot \sqrt{5} \cdot \sqrt{10}$

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

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

$x^{1} x^{2} \sqrt{3} \cdot \sqrt{5} \cdot \sqrt{10}$

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

$x^{1 + 2} \sqrt{3} \cdot \sqrt{5} \cdot \sqrt{10}$

Add $1$ and $2$ .

$x^{3} \sqrt{3} \cdot \sqrt{5} \cdot \sqrt{10}$

Step 6

Multiply $x^{3} \sqrt{3} \sqrt{5}$ .

Combine using the product rule for radicals.

$x^{3} \sqrt{5 \cdot 3} \cdot \sqrt{10}$

Multiply $5$ by $3$ .

$x^{3} \sqrt{15} \cdot \sqrt{10}$

Step 7

Multiply $x^{3} \sqrt{15} \sqrt{10}$ .

Combine using the product rule for radicals.

$x^{3} \sqrt{10 \cdot 15}$

Multiply $10$ by $15$ .

$x^{3} \sqrt{150}$

Step 8

Rewrite $150$ as $5^{2} \cdot 6$ .

Factor $25$ out of $150$ .

$x^{3} \sqrt{25 (6)}$

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

$x^{3} \sqrt{5^{2} \cdot 6}$

Step 9

Pull terms out from under the radical.

$x^{3} (5 \sqrt{6})$

Step 10

Move $5$ to the left of $x^{3}$ .

$5 x^{3} \sqrt{6}$

Simplify square root of 3x^4* square root of 5x^2* square root of 10

Related Questions

Support LCMGCF.com by disabling your adblocker.