Simplify 8x square root of 150x^5-9 square root of 150x^7

$8 x \sqrt{150 x^{5}} - 9 \sqrt{150 x^{7}}$

Step 1

Simplify each term.

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

Factor $25$ out of $150$ .

$8 x \sqrt{25 (6) x^{5}} - 9 \sqrt{150 x^{7}}$

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

$8 x \sqrt{5^{2} \cdot 6 x^{5}} - 9 \sqrt{150 x^{7}}$

Factor out $x^{4}$ .

$8 x \sqrt{5^{2} \cdot 6 (x^{4} x)} - 9 \sqrt{150 x^{7}}$

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

$8 x \sqrt{5^{2} \cdot 6 ({(x^{2})}^{2} x)} - 9 \sqrt{150 x^{7}}$

Move $6$ .

$8 x \sqrt{5^{2} {(x^{2})}^{2} \cdot 6 x} - 9 \sqrt{150 x^{7}}$

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

$8 x \sqrt{{(5 x^{2})}^{2} \cdot 6 x} - 9 \sqrt{150 x^{7}}$

Add parentheses.

$8 x \sqrt{{(5 x^{2})}^{2} \cdot (6 x)} - 9 \sqrt{150 x^{7}}$

Pull terms out from under the radical.

$8 x (5 x^{2} \sqrt{6 x}) - 9 \sqrt{150 x^{7}}$

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

Move $x^{2}$ .

$8 (x^{2} x) (5 \sqrt{6 x}) - 9 \sqrt{150 x^{7}}$

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

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

$8 (x^{2} x^{1}) (5 \sqrt{6 x}) - 9 \sqrt{150 x^{7}}$

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

$8 x^{2 + 1} (5 \sqrt{6 x}) - 9 \sqrt{150 x^{7}}$

Add $2$ and $1$ .

$8 x^{3} (5 \sqrt{6 x}) - 9 \sqrt{150 x^{7}}$

Multiply $5$ by $8$ .

$40 x^{3} \sqrt{6 x} - 9 \sqrt{150 x^{7}}$

Rewrite $150 x^{7}$ as ${(5 x^{3})}^{2} \cdot (6 x)$ .

Factor $25$ out of $150$ .

$40 x^{3} \sqrt{6 x} - 9 \sqrt{25 (6) x^{7}}$

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

$40 x^{3} \sqrt{6 x} - 9 \sqrt{5^{2} \cdot 6 x^{7}}$

Factor out $x^{6}$ .

$40 x^{3} \sqrt{6 x} - 9 \sqrt{5^{2} \cdot 6 (x^{6} x)}$

Rewrite $x^{6}$ as ${(x^{3})}^{2}$ .

$40 x^{3} \sqrt{6 x} - 9 \sqrt{5^{2} \cdot 6 ({(x^{3})}^{2} x)}$

Move $6$ .

$40 x^{3} \sqrt{6 x} - 9 \sqrt{5^{2} {(x^{3})}^{2} \cdot 6 x}$

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

$40 x^{3} \sqrt{6 x} - 9 \sqrt{{(5 x^{3})}^{2} \cdot 6 x}$

Add parentheses.

$40 x^{3} \sqrt{6 x} - 9 \sqrt{{(5 x^{3})}^{2} \cdot (6 x)}$

Pull terms out from under the radical.

$40 x^{3} \sqrt{6 x} - 9 (5 x^{3} \sqrt{6 x})$

Multiply $5$ by $- 9$ .

$40 x^{3} \sqrt{6 x} - 45 x^{3} \sqrt{6 x}$

Step 2

Subtract $45 x^{3} \sqrt{6 x}$ from $40 x^{3} \sqrt{6 x}$ .

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

Simplify 8x square root of 150x^5-9 square root of 150x^7

Related Questions

Support LCMGCF.com by disabling your adblocker.