Trigonometry Examples

\sqrt{(- 2^{2}) \cdot (- 1^{2})}

$\sqrt{(- 2^{2}) \cdot (- 1^{2})}$

Step 1

Multiply

- 1

$- 1$ by

- 1

$- 1$ by adding the exponents.

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Step 1.1

Move

- 1

$- 1$ .

\sqrt{- - 1 \cdot 2^{2} \cdot 1^{2}}

$\sqrt{- - 1 \cdot 2^{2} \cdot 1^{2}}$

Step 1.2

Multiply

- 1

$- 1$ by

- 1

$- 1$ .

\sqrt{{(- 1)}^{2} \cdot 2^{2} \cdot 1^{2}}

$\sqrt{{(- 1)}^{2} \cdot 2^{2} \cdot 1^{2}}$

\sqrt{{(- 1)}^{2} \cdot 2^{2} \cdot 1^{2}}

$\sqrt{{(- 1)}^{2} \cdot 2^{2} \cdot 1^{2}}$

Step 2

Rewrite

- 1

$- 1$ as

- 1 (1)

$- 1 (1)$ .

\sqrt{{(- 1 (1))}^{2} \cdot 2^{2} \cdot 1^{2}}

$\sqrt{{(- 1 (1))}^{2} \cdot 2^{2} \cdot 1^{2}}$

Step 3

Simplify the expression.

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Step 3.1

Apply the product rule to

- 1 (1)

$- 1 (1)$ .

\sqrt{{(- 1)}^{2} \cdot 1^{2} \cdot 2^{2} \cdot 1^{2}}

$\sqrt{{(- 1)}^{2} \cdot 1^{2} \cdot 2^{2} \cdot 1^{2}}$

Step 3.2

Raise

- 1

$- 1$ to the power of

2

$2$ .

\sqrt{1 \cdot 1^{2} \cdot 2^{2} \cdot 1^{2}}

$\sqrt{1 \cdot 1^{2} \cdot 2^{2} \cdot 1^{2}}$

Step 3.3

Multiply

1^{2}

$1^{2}$ by

1

$1$ .

\sqrt{1^{2} \cdot 2^{2} \cdot 1^{2}}

$\sqrt{1^{2} \cdot 2^{2} \cdot 1^{2}}$

\sqrt{1^{2} \cdot 2^{2} \cdot 1^{2}}

$\sqrt{1^{2} \cdot 2^{2} \cdot 1^{2}}$

Step 4

Multiply

1^{2}

$1^{2}$ by

1^{2}

$1^{2}$ by adding the exponents.

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Step 4.1

Move

1^{2}

$1^{2}$ .

\sqrt{1^{2} \cdot 1^{2} \cdot 2^{2}}

$\sqrt{1^{2} \cdot 1^{2} \cdot 2^{2}}$

Step 4.2

Use the power rule

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

\sqrt{1^{2 + 2} \cdot 2^{2}}

$\sqrt{1^{2 + 2} \cdot 2^{2}}$

Step 4.3

Add

2

$2$ and

2

$2$ .

\sqrt{1^{4} \cdot 2^{2}}

$\sqrt{1^{4} \cdot 2^{2}}$

\sqrt{1^{4} \cdot 2^{2}}

$\sqrt{1^{4} \cdot 2^{2}}$

Step 5

One to any power is one.

\sqrt{1 \cdot 2^{2}}

$\sqrt{1 \cdot 2^{2}}$

Step 6

Raise

2

$2$ to the power of

2

$2$ .

\sqrt{1 \cdot 4}

$\sqrt{1 \cdot 4}$

Step 7

Multiply

4

$4$ by

1

$1$ .

\sqrt{4}

$\sqrt{4}$

Step 8

Rewrite

4

$4$ as

2^{2}

$2^{2}$ .

\sqrt{2^{2}}

$\sqrt{2^{2}}$

Step 9

Pull terms out from under the radical, assuming positive real numbers.

2

$2$