Solve sqrt{[(1.3)^{2}-(0.7)^{2}+3.2]^2:11^2*5+[(2.8)^2-0.23]*10^2}

$$\sqrt { [ ( 1.3 ) ^ { 2 } - ( 0.7 ) ^ { 2 } + 3.2 ] ^ { 2 } : 11 ^ { 2 } \cdot 5 + [ ( 2.8 ) ^ { 2 } - 0.23 ] \cdot 10 ^ { 2 } }$$

Evaluate

$$\frac{\sqrt{19045}}{5}\approx 27.600724628$$

Solution Steps

Calculate 1.3 to the power of 2 and get 1.69.

$$\sqrt{\frac{\left(1.69-0.7^{2}+3.2\right)^{2}}{11^{2}}\times 5+\left(2.8^{2}-0.23\right)\times 10^{2}}$$

Calculate 0.7 to the power of 2 and get 0.49.

$$\sqrt{\frac{\left(1.69-0.49+3.2\right)^{2}}{11^{2}}\times 5+\left(2.8^{2}-0.23\right)\times 10^{2}}$$

Subtract 0.49 from 1.69 to get 1.2.

$$\sqrt{\frac{\left(1.2+3.2\right)^{2}}{11^{2}}\times 5+\left(2.8^{2}-0.23\right)\times 10^{2}}$$

Add 1.2 and 3.2 to get 4.4.

$$\sqrt{\frac{4.4^{2}}{11^{2}}\times 5+\left(2.8^{2}-0.23\right)\times 10^{2}}$$

Calculate 4.4 to the power of 2 and get 19.36.

$$\sqrt{\frac{19.36}{11^{2}}\times 5+\left(2.8^{2}-0.23\right)\times 10^{2}}$$

Calculate 11 to the power of 2 and get 121.

$$\sqrt{\frac{19.36}{121}\times 5+\left(2.8^{2}-0.23\right)\times 10^{2}}$$

Expand \frac{19.36}{121} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{1936}{12100}\times 5+\left(2.8^{2}-0.23\right)\times 10^{2}}$$

Reduce the fraction \frac{1936}{12100} to lowest terms by extracting and canceling out 484.

$$\sqrt{\frac{4}{25}\times 5+\left(2.8^{2}-0.23\right)\times 10^{2}}$$

Multiply \frac{4}{25} and 5 to get \frac{4}{5}.

$$\sqrt{\frac{4}{5}+\left(2.8^{2}-0.23\right)\times 10^{2}}$$

Calculate 2.8 to the power of 2 and get 7.84.

$$\sqrt{\frac{4}{5}+\left(7.84-0.23\right)\times 10^{2}}$$

Subtract 0.23 from 7.84 to get 7.61.

$$\sqrt{\frac{4}{5}+7.61\times 10^{2}}$$

Calculate 10 to the power of 2 and get 100.

$$\sqrt{\frac{4}{5}+7.61\times 100}$$

Multiply 7.61 and 100 to get 761.

$$\sqrt{\frac{4}{5}+761}$$

Add \frac{4}{5} and 761 to get \frac{3809}{5}.

$$\sqrt{\frac{3809}{5}}$$

Rewrite the square root of the division \sqrt{\frac{3809}{5}} as the division of square roots \frac{\sqrt{3809}}{\sqrt{5}}.

$$\frac{\sqrt{3809}}{\sqrt{5}}$$

Rationalize the denominator of \frac{\sqrt{3809}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{\sqrt{3809}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{\sqrt{3809}\sqrt{5}}{5}$$

To multiply \sqrt{3809} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{\sqrt{19045}}{5}$$