Simplify 2q square root of 700q^4-q square root of 175q^4

$2 q \sqrt{700 q^{4}} - q \sqrt{175 q^{4}}$

Simplify each term.

Rewrite $700 q^{4}$ as ${(10 q^{2})}^{2} \cdot 7$ .

Factor $100$ out of $700$ .

$2 q \sqrt{100 (7) q^{4}} - q \sqrt{175 q^{4}}$

Rewrite $100$ as $10^{2}$ .

$2 q \sqrt{10^{2} \cdot 7 q^{4}} - q \sqrt{175 q^{4}}$

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

$2 q \sqrt{10^{2} \cdot 7 {(q^{2})}^{2}} - q \sqrt{175 q^{4}}$

Move $7$ .

$2 q \sqrt{10^{2} {(q^{2})}^{2} \cdot 7} - q \sqrt{175 q^{4}}$

Rewrite $10^{2} {(q^{2})}^{2}$ as ${(10 q^{2})}^{2}$ .

$2 q \sqrt{{(10 q^{2})}^{2} \cdot 7} - q \sqrt{175 q^{4}}$

Pull terms out from under the radical.

$2 q (10 q^{2} \sqrt{7}) - q \sqrt{175 q^{4}}$

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

Move $q^{2}$ .

$2 (q^{2} q) (10 \sqrt{7}) - q \sqrt{175 q^{4}}$

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

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

$2 (q^{2} q^{1}) (10 \sqrt{7}) - q \sqrt{175 q^{4}}$

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

$2 q^{2 + 1} (10 \sqrt{7}) - q \sqrt{175 q^{4}}$

Add $2$ and $1$ .

$2 q^{3} (10 \sqrt{7}) - q \sqrt{175 q^{4}}$

Multiply $10$ by $2$ .

$20 q^{3} \sqrt{7} - q \sqrt{175 q^{4}}$

Rewrite $175 q^{4}$ as ${(5 q^{2})}^{2} \cdot 7$ .

Factor $25$ out of $175$ .

$20 q^{3} \sqrt{7} - q \sqrt{25 (7) q^{4}}$

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

$20 q^{3} \sqrt{7} - q \sqrt{5^{2} \cdot 7 q^{4}}$

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

$20 q^{3} \sqrt{7} - q \sqrt{5^{2} \cdot 7 {(q^{2})}^{2}}$

Move $7$ .

$20 q^{3} \sqrt{7} - q \sqrt{5^{2} {(q^{2})}^{2} \cdot 7}$

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

$20 q^{3} \sqrt{7} - q \sqrt{{(5 q^{2})}^{2} \cdot 7}$

Pull terms out from under the radical.

$20 q^{3} \sqrt{7} - q (5 q^{2} \sqrt{7})$

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

Move $q^{2}$ .

$20 q^{3} \sqrt{7} - (q^{2} q) (5 \sqrt{7})$

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

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

$20 q^{3} \sqrt{7} - (q^{2} q^{1}) (5 \sqrt{7})$

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

$20 q^{3} \sqrt{7} - q^{2 + 1} (5 \sqrt{7})$

Add $2$ and $1$ .

$20 q^{3} \sqrt{7} - q^{3} (5 \sqrt{7})$

Multiply $5$ by $- 1$ .

$20 q^{3} \sqrt{7} - 5 q^{3} \sqrt{7}$

Subtract $5 q^{3} \sqrt{7}$ from $20 q^{3} \sqrt{7}$ .

$15 q^{3} \sqrt{7}$

Simplify 2q square root of 700q^4-q square root of 175q^4

Related Questions

Support LCMGCF.com by disabling your adblocker.