Solve frac{3sqrt{7}}{sqrt{4}}*frac{sqrt{133}}{14}

$$\frac { 3 \sqrt { 7 } } { \sqrt { 4 } } \times \frac { \sqrt { 133 } } { 14 }$$

Evaluate

$$\frac{3\sqrt{19}}{4}\approx 3.269174208$$

Solution Steps

Calculate the square root of 4 and get 2.

$$\frac{3\sqrt{7}}{2}\times \frac{\sqrt{133}}{14}$$

Multiply \frac{3\sqrt{7}}{2} times \frac{\sqrt{133}}{14} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\sqrt{7}\sqrt{133}}{2\times 14}$$

Factor 133=7\times 19. Rewrite the square root of the product \sqrt{7\times 19} as the product of square roots \sqrt{7}\sqrt{19}.

$$\frac{3\sqrt{7}\sqrt{7}\sqrt{19}}{2\times 14}$$

Multiply \sqrt{7} and \sqrt{7} to get 7.

$$\frac{3\times 7\sqrt{19}}{2\times 14}$$

Multiply 3 and 7 to get 21.

$$\frac{21\sqrt{19}}{2\times 14}$$

Multiply 2 and 14 to get 28.

$$\frac{21\sqrt{19}}{28}$$

Divide 21\sqrt{19} by 28 to get \frac{3}{4}\sqrt{19}.

$$\frac{3}{4}\sqrt{19}$$