Simplify the Radical Expression square root of 32h+4 square root of 98h-3 square root of 50h

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Algebra

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

Simplify each term.

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

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Factor $16$ out of $32$ .

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

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

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

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

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

Add parentheses.

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

Pull terms out from under the radical.

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

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

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

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

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

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

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Factor $49$ out of $98$ .

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

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

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

Add parentheses.

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

Pull terms out from under the radical.

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

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

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

Multiply $7$ by $4$ .

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

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

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Factor $25$ out of $50$ .

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

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

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

Add parentheses.

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

Pull terms out from under the radical.

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

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

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

Multiply $5$ by $- 3$ .

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

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

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

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

$17 \sqrt{2 h}$

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