Evaluate square root of 2*( square root of 2)/2

$\sqrt{2} \cdot \frac{\sqrt{2}}{2}$

Step 1

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

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

$\frac{\sqrt{2} \sqrt{2}}{2}$

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

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

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

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

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

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

Add $1$ and $1$ .

$\frac{{\sqrt{2}}^{2}}{2}$

Step 2

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

$\frac{2}{2}$

Step 3

Divide $2$ by $2$ .

$1$