Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Factor $16$ out of $80$ .

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

Step 1.1.2

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

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

Step 1.1.3

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

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

Step 1.1.4

Add parentheses.

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

Step 1.2

Pull terms out from under the radical.

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

Step 1.3

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

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Step 1.3.1

Move $2^{2}$ .

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

Step 1.3.2

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

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Step 1.3.2.1

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

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

Step 1.3.2.2

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

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

Step 1.3.3

Add $2$ and $1$ .

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

Step 1.4

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

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

Step 1.5

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

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Step 1.5.1

Factor $25$ out of $125$ .

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

Step 1.5.2

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

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

Step 1.5.3

Add parentheses.

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

Step 1.6

Pull terms out from under the radical.

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

Step 1.7

Multiply $5$ by $- 7$ .

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

Step 2

Simplify by adding terms.

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Step 2.1

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

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

Step 2.2

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

$- 26 \sqrt{5 a}$