Simplify the Radical Expression square root of 63- square root of 700- square root of 112

$\sqrt{63} - \sqrt{700} - \sqrt{112}$

Step 1

Simplify each term.

Rewrite $63$ as $3^{2} \cdot 7$ .

Factor $9$ out of $63$ .

$\sqrt{9 (7)} - \sqrt{700} - \sqrt{112}$

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

$\sqrt{3^{2} \cdot 7} - \sqrt{700} - \sqrt{112}$

Pull terms out from under the radical.

$| 3 | \sqrt{7} - \sqrt{700} - \sqrt{112}$

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

$3 \sqrt{7} - \sqrt{700} - \sqrt{112}$

Rewrite $700$ as $10^{2} \cdot 7$ .

Factor $100$ out of $700$ .

$3 \sqrt{7} - \sqrt{100 (7)} - \sqrt{112}$

Rewrite $100$ as $10^{2}$ .

$3 \sqrt{7} - \sqrt{10^{2} \cdot 7} - \sqrt{112}$

Pull terms out from under the radical.

$3 \sqrt{7} - (| 10 | \sqrt{7}) - \sqrt{112}$

The absolute value is the distance between a number and zero. The distance between $0$ and $10$ is $10$ .

$3 \sqrt{7} - (10 \sqrt{7}) - \sqrt{112}$

Multiply $10$ by $- 1$ .

$3 \sqrt{7} - 10 \sqrt{7} - \sqrt{112}$

Rewrite $112$ as $4^{2} \cdot 7$ .

Factor $16$ out of $112$ .

$3 \sqrt{7} - 10 \sqrt{7} - \sqrt{16 (7)}$

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

$3 \sqrt{7} - 10 \sqrt{7} - \sqrt{4^{2} \cdot 7}$

Pull terms out from under the radical.

$3 \sqrt{7} - 10 \sqrt{7} - (| 4 | \sqrt{7})$

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

$3 \sqrt{7} - 10 \sqrt{7} - (4 \sqrt{7})$

Multiply $4$ by $- 1$ .

$3 \sqrt{7} - 10 \sqrt{7} - 4 \sqrt{7}$

Step 2

Subtract $10 \sqrt{7}$ from $3 \sqrt{7}$ .

$- 7 \sqrt{7} - 4 \sqrt{7}$

Step 3

Subtract $4 \sqrt{7}$ from $- 7 \sqrt{7}$ .

$- 11 \sqrt{7}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$- 11 \sqrt{7}$

Decimal Form:

$- 29.10326442 \dots$

Simplify the Radical Expression square root of 63- square root of 700- square root of 112

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