Simplify the Radical Expression 8 fourth root of 48-5 square root of 90+9 fourth root of 3

$8 \sqrt[4]{48} - 5 \sqrt{90} + 9 \sqrt[4]{3}$

Simplify each term.

Rewrite $48$ as $2^{4} \cdot 3$ .

Factor $16$ out of $48$ .

$8 \sqrt[4]{16 (3)} - 5 \sqrt{90} + 9 \sqrt[4]{3}$

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

$8 \sqrt[4]{2^{4} \cdot 3} - 5 \sqrt{90} + 9 \sqrt[4]{3}$

Pull terms out from under the radical.

$8 (| 2 | \sqrt[4]{3}) - 5 \sqrt{90} + 9 \sqrt[4]{3}$

The absolute value is the distance between a number and zero. The distance between $0$ and $2$ is $2$ .

$8 (2 \sqrt[4]{3}) - 5 \sqrt{90} + 9 \sqrt[4]{3}$

Multiply $2$ by $8$ .

$16 \sqrt[4]{3} - 5 \sqrt{90} + 9 \sqrt[4]{3}$

Rewrite $90$ as $3^{2} \cdot 10$ .

Factor $9$ out of $90$ .

$16 \sqrt[4]{3} - 5 \sqrt{9 (10)} + 9 \sqrt[4]{3}$

Rewrite $9$ as $3^{2}$ .

$16 \sqrt[4]{3} - 5 \sqrt{3^{2} \cdot 10} + 9 \sqrt[4]{3}$

Pull terms out from under the radical.

$16 \sqrt[4]{3} - 5 (| 3 | \sqrt{10}) + 9 \sqrt[4]{3}$

The absolute value is the distance between a number and zero. The distance between $0$ and $3$ is $3$ .

$16 \sqrt[4]{3} - 5 (3 \sqrt{10}) + 9 \sqrt[4]{3}$

Multiply $3$ by $- 5$ .

$16 \sqrt[4]{3} - 15 \sqrt{10} + 9 \sqrt[4]{3}$

Add $16 \sqrt[4]{3}$ and $9 \sqrt[4]{3}$ .

$25 \sqrt[4]{3} - 15 \sqrt{10}$

The result can be shown in multiple forms.

Exact Form:

$25 \sqrt[4]{3} - 15 \sqrt{10}$

Decimal Form:

$- 14.53231457 \dots$