Trigonometry Examples

$\sqrt{10 (10 - 6) (10 - 7) (10 - 7)}$

Step 1

Raise $10 - 7$ to the power of $1$ .

$\sqrt{10 (10 - 6) ({(10 - 7)}^{1} (10 - 7))}$

Step 2

Raise $10 - 7$ to the power of $1$ .

$\sqrt{10 (10 - 6) ({(10 - 7)}^{1} {(10 - 7)}^{1})}$

Step 3

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

$\sqrt{10 (10 - 6) {(10 - 7)}^{1 + 1}}$

Step 4

Add $1$ and $1$ .

$\sqrt{10 (10 - 6) {(10 - 7)}^{2}}$

Step 5

Subtract $6$ from $10$ .

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

Step 6

Multiply $10$ by $4$ .

$\sqrt{40 {(10 - 7)}^{2}}$

Step 7

Subtract $7$ from $10$ .

$\sqrt{40 \cdot 3^{2}}$

Step 8

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

$\sqrt{40 \cdot 9}$

Step 9

Multiply $40$ by $9$ .

$\sqrt{360}$

Step 10

Rewrite $360$ as $6^{2} \cdot 10$ .

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Step 10.1

Factor $36$ out of $360$ .

$\sqrt{36 (10)}$

Step 10.2

Rewrite $36$ as $6^{2}$ .

$\sqrt{6^{2} \cdot 10}$

Step 11

Pull terms out from under the radical.

$6 \sqrt{10}$

Step 12

The result can be shown in multiple forms.

Exact Form:

$6 \sqrt{10}$

Decimal Form:

$18.97366596 \dots$