Simplify (- square root of 8* square root of 2)+ square root of -36

$(- \sqrt{8} \cdot \sqrt{2}) + \sqrt{- 36}$

Step 1

Rewrite $8$ as $2^{2} \cdot 2$ .

Factor $4$ out of $8$ .

$- \sqrt{4 (2)} \cdot \sqrt{2} + \sqrt{- 36}$

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

$- \sqrt{2^{2} \cdot 2} \cdot \sqrt{2} + \sqrt{- 36}$

Step 2

Pull terms out from under the radical.

$- (2 \sqrt{2}) \cdot \sqrt{2} + \sqrt{- 36}$

Step 3

Multiply $2$ by $- 1$ .

$- 2 \sqrt{2} \cdot \sqrt{2} + \sqrt{- 36}$

Step 4

Multiply $- 2 \sqrt{2} \sqrt{2}$ .

Raise $\sqrt{2}$ to the power of $1$ .

$- 2 ({\sqrt{2}}^{1} \sqrt{2}) + \sqrt{- 36}$

Raise $\sqrt{2}$ to the power of $1$ .

$- 2 ({\sqrt{2}}^{1} {\sqrt{2}}^{1}) + \sqrt{- 36}$

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

$- 2 {\sqrt{2}}^{1 + 1} + \sqrt{- 36}$

Add $1$ and $1$ .

$- 2 {\sqrt{2}}^{2} + \sqrt{- 36}$

Step 5

Rewrite ${\sqrt{2}}^{2}$ as $2$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2}$ as $2^{\frac{1}{2}}$ .

$- 2 {(2^{\frac{1}{2}})}^{2} + \sqrt{- 36}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$- 2 \cdot 2^{\frac{1}{2} \cdot 2} + \sqrt{- 36}$

Combine $\frac{1}{2}$ and $2$ .

$- 2 \cdot 2^{\frac{2}{2}} + \sqrt{- 36}$

Cancel the common factor of $2$ .

Cancel the common factor.

$- 2 \cdot 2^{\frac{2}{2}} + \sqrt{- 36}$

Rewrite the expression.

$- 2 \cdot 2^{1} + \sqrt{- 36}$

Evaluate the exponent.

$- 2 \cdot 2 + \sqrt{- 36}$

Step 6

Multiply $- 2$ by $2$ .

$- 4 + \sqrt{- 36}$

Step 7

Rewrite $- 36$ as $- 1 (36)$ .

$- 4 + \sqrt{- 1 (36)}$

Step 8

Rewrite $\sqrt{- 1 (36)}$ as $\sqrt{- 1} \cdot \sqrt{36}$ .

$- 4 + \sqrt{- 1} \cdot \sqrt{36}$

Step 9

Rewrite $\sqrt{- 1}$ as $i$ .

$- 4 + i \cdot \sqrt{36}$

Step 10

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

$- 4 + i \cdot \sqrt{6^{2}}$

Step 11

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

$- 4 + i \cdot 6$

Step 12

Move $6$ to the left of $i$ .

$- 4 + 6 i$

Simplify (- square root of 8* square root of 2)+ square root of -36

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