Evaluate 2(2)^(1/2)

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

Step 1

Multiply $2$ by ${(2)}^{\frac{1}{2}}$ .

Raise $2$ to the power of $1$ .

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

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

$2^{1 + \frac{1}{2}}$

Step 2

Write $1$ as a fraction with a common denominator.

$2^{\frac{2}{2} + \frac{1}{2}}$

Step 3

Combine the numerators over the common denominator.

$2^{\frac{2 + 1}{2}}$

Step 4

Add $2$ and $1$ .

$2^{\frac{3}{2}}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$2^{\frac{3}{2}}$

Decimal Form:

$2.82842712 \dots$