Solve (1)sqrt{(sqrt{2})^2+(sqrt{7})^2}-sqrt{(sqrt{13})^2-(-3)^2}

$$( 1 ) \sqrt { ( \sqrt { 2 } ) ^ { 2 } + ( \sqrt { 7 } ) ^ { 2 } } - \sqrt { ( \sqrt { 13 } ) ^ { 2 } - ( - 3 ) ^ { 2 } }$$

Evaluate

$$1$$

Solution Steps

The square of \sqrt{2} is 2.

$$1\sqrt{2+\left(\sqrt{7}\right)^{2}}-\sqrt{\left(\sqrt{13}\right)^{2}-\left(-3\right)^{2}}$$

The square of \sqrt{7} is 7.

$$1\sqrt{2+7}-\sqrt{\left(\sqrt{13}\right)^{2}-\left(-3\right)^{2}}$$

Add 2 and 7 to get 9.

$$1\sqrt{9}-\sqrt{\left(\sqrt{13}\right)^{2}-\left(-3\right)^{2}}$$

Calculate the square root of 9 and get 3.

$$1\times 3-\sqrt{\left(\sqrt{13}\right)^{2}-\left(-3\right)^{2}}$$

Multiply 1 and 3 to get 3.

$$3-\sqrt{\left(\sqrt{13}\right)^{2}-\left(-3\right)^{2}}$$

The square of \sqrt{13} is 13.

$$3-\sqrt{13-\left(-3\right)^{2}}$$

Calculate -3 to the power of 2 and get 9.

$$3-\sqrt{13-9}$$

Subtract 9 from 13 to get 4.

$$3-\sqrt{4}$$

Calculate the square root of 4 and get 2.

$$3-2$$

Subtract 2 from 3 to get 1.

$$1$$

Factor

$$1$$