Evaluate square root of -20* square root of 5

$\sqrt{- 20} \cdot \sqrt{5}$

Step 1

Rewrite $- 20$ as $- 1 (20)$ .

$\sqrt{- 1 (20)} \cdot \sqrt{5}$

Step 2

Rewrite $\sqrt{- 1 (20)}$ as $\sqrt{- 1} \cdot \sqrt{20}$ .

$\sqrt{- 1} \cdot \sqrt{20} \cdot \sqrt{5}$

Step 3

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

$i \cdot \sqrt{20} \cdot \sqrt{5}$

Step 4

Rewrite $20$ as $2^{2} \cdot 5$ .

Factor $4$ out of $20$ .

$i \cdot \sqrt{4 (5)} \cdot \sqrt{5}$

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

$i \cdot \sqrt{2^{2} \cdot 5} \cdot \sqrt{5}$

Step 5

Pull terms out from under the radical.

$i \cdot (2 \sqrt{5}) \cdot \sqrt{5}$

Step 6

Move $2$ to the left of $i$ .

$2 \cdot i \sqrt{5} \cdot \sqrt{5}$

Step 7

Multiply $2 i \sqrt{5} \sqrt{5}$ .

Raise $\sqrt{5}$ to the power of $1$ .

$2 i ({\sqrt{5}}^{1} \sqrt{5})$

Raise $\sqrt{5}$ to the power of $1$ .

$2 i ({\sqrt{5}}^{1} {\sqrt{5}}^{1})$

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

$2 i {\sqrt{5}}^{1 + 1}$

Add $1$ and $1$ .

$2 i {\sqrt{5}}^{2}$

Step 8

Rewrite ${\sqrt{5}}^{2}$ as $5$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5}$ as $5^{\frac{1}{2}}$ .

$2 i {(5^{\frac{1}{2}})}^{2}$

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

$2 i \cdot 5^{\frac{1}{2} \cdot 2}$

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

$2 i \cdot 5^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$2 i \cdot 5^{\frac{2}{2}}$

Rewrite the expression.

$2 i \cdot 5^{1}$

Evaluate the exponent.

$2 i \cdot 5$

Step 9

Multiply $5$ by $2$ .

$10 i$

Evaluate square root of -20* square root of 5

Related Questions

Support LCMGCF.com by disabling your adblocker.