Solve (frac{3sqrt{21}}{14})^2

$$( \frac { 3 \sqrt { 21 } } { 14 } ) ^ { 2 }$$

Evaluate

$$\frac{27}{28}\approx 0.964285714$$

Solution Steps

To raise \frac{3\sqrt{21}}{14} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(3\sqrt{21}\right)^{2}}{14^{2}}$$

Expand \left(3\sqrt{21}\right)^{2}.

$$\frac{3^{2}\left(\sqrt{21}\right)^{2}}{14^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{9\left(\sqrt{21}\right)^{2}}{14^{2}}$$

The square of \sqrt{21} is 21.

$$\frac{9\times 21}{14^{2}}$$

Multiply 9 and 21 to get 189.

$$\frac{189}{14^{2}}$$

Calculate 14 to the power of 2 and get 196.

$$\frac{189}{196}$$

Reduce the fraction \frac{189}{196} to lowest terms by extracting and canceling out 7.

$$\frac{27}{28}$$

Factor

$$\frac{3 ^ {3}}{2 ^ {2} \cdot 7} = 0.9642857142857143$$