Algebra Examples

$\sqrt{32 h} + 4 \sqrt{98 h} - 3 \sqrt{50 h}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $32 h$ as ${(2^{2})}^{2} \cdot (2 h)$ .

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Step 1.1.1

Factor $16$ out of $32$ .

$\sqrt{16 (2) h} + 4 \sqrt{98 h} - 3 \sqrt{50 h}$

Step 1.1.2

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

$\sqrt{4^{2} \cdot 2 h} + 4 \sqrt{98 h} - 3 \sqrt{50 h}$

Step 1.1.3

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

$\sqrt{{(2^{2})}^{2} \cdot 2 h} + 4 \sqrt{98 h} - 3 \sqrt{50 h}$

Step 1.1.4

Add parentheses.

$\sqrt{{(2^{2})}^{2} \cdot (2 h)} + 4 \sqrt{98 h} - 3 \sqrt{50 h}$

Step 1.2

Pull terms out from under the radical.

$| 2^{2} | \sqrt{2 h} + 4 \sqrt{98 h} - 3 \sqrt{50 h}$

Step 1.3

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

$| 4 | \sqrt{2 h} + 4 \sqrt{98 h} - 3 \sqrt{50 h}$

Step 1.4

The absolute value is the distance between a number and zero. The distance between $0$ and $4$ is $4$ .

$4 \sqrt{2 h} + 4 \sqrt{98 h} - 3 \sqrt{50 h}$

Step 1.5

Rewrite $98 h$ as $7^{2} \cdot (2 h)$ .

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Step 1.5.1

Factor $49$ out of $98$ .

$4 \sqrt{2 h} + 4 \sqrt{49 (2) h} - 3 \sqrt{50 h}$

Step 1.5.2

Rewrite $49$ as $7^{2}$ .

$4 \sqrt{2 h} + 4 \sqrt{7^{2} \cdot 2 h} - 3 \sqrt{50 h}$

Step 1.5.3

Add parentheses.

$4 \sqrt{2 h} + 4 \sqrt{7^{2} \cdot (2 h)} - 3 \sqrt{50 h}$

Step 1.6

Pull terms out from under the radical.

$4 \sqrt{2 h} + 4 (| 7 | \sqrt{2 h}) - 3 \sqrt{50 h}$

Step 1.7

The absolute value is the distance between a number and zero. The distance between $0$ and $7$ is $7$ .

$4 \sqrt{2 h} + 4 (7 \sqrt{2 h}) - 3 \sqrt{50 h}$

Step 1.8

Multiply $7$ by $4$ .

$4 \sqrt{2 h} + 28 \sqrt{2 h} - 3 \sqrt{50 h}$

Step 1.9

Rewrite $50 h$ as $5^{2} \cdot (2 h)$ .

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Step 1.9.1

Factor $25$ out of $50$ .

$4 \sqrt{2 h} + 28 \sqrt{2 h} - 3 \sqrt{25 (2) h}$

Step 1.9.2

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

$4 \sqrt{2 h} + 28 \sqrt{2 h} - 3 \sqrt{5^{2} \cdot 2 h}$

Step 1.9.3

Add parentheses.

$4 \sqrt{2 h} + 28 \sqrt{2 h} - 3 \sqrt{5^{2} \cdot (2 h)}$

Step 1.10

Pull terms out from under the radical.

$4 \sqrt{2 h} + 28 \sqrt{2 h} - 3 (| 5 | \sqrt{2 h})$

Step 1.11

The absolute value is the distance between a number and zero. The distance between $0$ and $5$ is $5$ .

$4 \sqrt{2 h} + 28 \sqrt{2 h} - 3 (5 \sqrt{2 h})$

Step 1.12

Multiply $5$ by $- 3$ .

$4 \sqrt{2 h} + 28 \sqrt{2 h} - 15 \sqrt{2 h}$

Step 2

Add $4 \sqrt{2 h}$ and $28 \sqrt{2 h}$ .

$32 \sqrt{2 h} - 15 \sqrt{2 h}$

Step 3

Subtract $15 \sqrt{2 h}$ from $32 \sqrt{2 h}$ .

$17 \sqrt{2 h}$