Solve (-sqrt{7})^2+sqrt{(7/10)^2}div(sqrt{0.1})^2-sqrt{121}

$$( - \sqrt { 7 } ) ^ { 2 } + \sqrt { ( \frac { 7 } { 10 } ) ^ { 2 } } \div ( \sqrt { 0.1 } ) ^ { 2 } - \sqrt { 121 }$$

Evaluate

$$3$$

Solution Steps

Calculate -\sqrt{7} to the power of 2 and get \left(\sqrt{7}\right)^{2}.

$$\left(\sqrt{7}\right)^{2}+\frac{\sqrt{\left(\frac{7}{10}\right)^{2}}}{\left(\sqrt{0.1}\right)^{2}}-\sqrt{121}$$

Calculate \frac{7}{10} to the power of 2 and get \frac{49}{100}.

$$\left(\sqrt{7}\right)^{2}+\frac{\sqrt{\frac{49}{100}}}{\left(\sqrt{0.1}\right)^{2}}-\sqrt{121}$$

Rewrite the square root of the division \frac{49}{100} as the division of square roots \frac{\sqrt{49}}{\sqrt{100}}. Take the square root of both numerator and denominator.

$$\left(\sqrt{7}\right)^{2}+\frac{\frac{7}{10}}{\left(\sqrt{0.1}\right)^{2}}-\sqrt{121}$$

The square of \sqrt{0.1} is 0.1.

$$\left(\sqrt{7}\right)^{2}+\frac{\frac{7}{10}}{0.1}-\sqrt{121}$$

Express \frac{\frac{7}{10}}{0.1} as a single fraction.

$$\left(\sqrt{7}\right)^{2}+\frac{7}{10\times 0.1}-\sqrt{121}$$

Multiply 10 and 0.1 to get 1.

$$\left(\sqrt{7}\right)^{2}+\frac{7}{1}-\sqrt{121}$$

Divide 7 by 1 to get 7.

$$\left(\sqrt{7}\right)^{2}+7-\sqrt{121}$$

Calculate the square root of 121 and get 11.

$$\left(\sqrt{7}\right)^{2}+7-11$$

Subtract 11 from 7 to get -4.

$$\left(\sqrt{7}\right)^{2}-4$$

The square of \sqrt{7} is 7.

$$7-4$$

Subtract 4 from 7 to get 3.

$$3$$

Factor

$$3$$