Solve 0,64150/sqrt{(frac{2{sqrt{2}})^2}}

$$0,64 \frac { 150 } { \sqrt { ( \frac { 2 } { \sqrt { 2 } } ) ^ { 2 } } }$$

Evaluate

$$48\sqrt{2}\approx 67.882250994$$

Solution Steps

Rationalize the denominator of \frac{2}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$0,64\times \frac{150}{\sqrt{\left(\frac{2\sqrt{2}}{\left(\sqrt{2}\right)^{2}}\right)^{2}}}$$

The square of \sqrt{2} is 2.

$$0,64\times \frac{150}{\sqrt{\left(\frac{2\sqrt{2}}{2}\right)^{2}}}$$

Cancel out 2 and 2.

$$0,64\times \frac{150}{\sqrt{\left(\sqrt{2}\right)^{2}}}$$

The square of \sqrt{2} is 2.

$$0,64\times \frac{150}{\sqrt{2}}$$

Rationalize the denominator of \frac{150}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$0,64\times \frac{150\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$0,64\times \frac{150\sqrt{2}}{2}$$

Divide 150\sqrt{2} by 2 to get 75\sqrt{2}.

$$0,64\times 75\sqrt{2}$$

Multiply 0,64 and 75 to get 48.

$$48\sqrt{2}$$