Combine square root of 5a+2 square root of 80a-7 square root of 125a

$\sqrt{5 a} + 2 \sqrt{80 a} - 7 \sqrt{125 a}$

Step 1

Simplify each term.

Rewrite $80 a$ as ${(2^{2})}^{2} \cdot (5 a)$ .

Factor $16$ out of $80$ .

$\sqrt{5 a} + 2 \sqrt{16 (5) a} - 7 \sqrt{125 a}$

Rewrite $16$ as $4^{2}$ .

$\sqrt{5 a} + 2 \sqrt{4^{2} \cdot 5 a} - 7 \sqrt{125 a}$

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

$\sqrt{5 a} + 2 \sqrt{{(2^{2})}^{2} \cdot 5 a} - 7 \sqrt{125 a}$

Add parentheses.

$\sqrt{5 a} + 2 \sqrt{{(2^{2})}^{2} \cdot (5 a)} - 7 \sqrt{125 a}$

Pull terms out from under the radical.

$\sqrt{5 a} + 2 (2^{2} \sqrt{5 a}) - 7 \sqrt{125 a}$

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

Move $2^{2}$ .

$\sqrt{5 a} + 2^{2} \cdot 2 \sqrt{5 a} - 7 \sqrt{125 a}$

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

Raise $2$ to the power of $1$ .

$\sqrt{5 a} + 2^{2} \cdot 2^{1} \sqrt{5 a} - 7 \sqrt{125 a}$

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

$\sqrt{5 a} + 2^{2 + 1} \sqrt{5 a} - 7 \sqrt{125 a}$

Add $2$ and $1$ .

$\sqrt{5 a} + 2^{3} \sqrt{5 a} - 7 \sqrt{125 a}$

Raise $2$ to the power of $3$ .

$\sqrt{5 a} + 8 \sqrt{5 a} - 7 \sqrt{125 a}$

Rewrite $125 a$ as $5^{2} \cdot (5 a)$ .

Factor $25$ out of $125$ .

$\sqrt{5 a} + 8 \sqrt{5 a} - 7 \sqrt{25 (5) a}$

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

$\sqrt{5 a} + 8 \sqrt{5 a} - 7 \sqrt{5^{2} \cdot 5 a}$

Add parentheses.

$\sqrt{5 a} + 8 \sqrt{5 a} - 7 \sqrt{5^{2} \cdot (5 a)}$

Pull terms out from under the radical.

$\sqrt{5 a} + 8 \sqrt{5 a} - 7 (5 \sqrt{5 a})$

Multiply $5$ by $- 7$ .

$\sqrt{5 a} + 8 \sqrt{5 a} - 35 \sqrt{5 a}$

Step 2

Simplify by adding terms.

Add $\sqrt{5 a}$ and $8 \sqrt{5 a}$ .

$9 \sqrt{5 a} - 35 \sqrt{5 a}$

Subtract $35 \sqrt{5 a}$ from $9 \sqrt{5 a}$ .

$- 26 \sqrt{5 a}$