Solve sqrt{9}+(1/2)^-1-sqrt{2}sin45^circ+(sqrt{3}-2)^0

$$\sqrt { 9 } + ( \frac { 1 } { 2 } ) ^ { - 1 } - \sqrt { 2 } \sin 45 ^ { \circ } + ( \sqrt { 3 } - 2 ) ^ { 0 }$$

Evaluate

$$5$$

Solution Steps

Calculate the square root of 9 and get 3.

$$3+\left(\frac{1}{2}\right)^{-1}-\sqrt{2}\sin(45)+\left(\sqrt{3}-2\right)^{0}$$

Calculate \frac{1}{2} to the power of -1 and get 2.

$$3+2-\sqrt{2}\sin(45)+\left(\sqrt{3}-2\right)^{0}$$

Add 3 and 2 to get 5.

$$5-\sqrt{2}\sin(45)+\left(\sqrt{3}-2\right)^{0}$$

Get the value of \sin(45) from trigonometric values table.

$$5-\sqrt{2}\times \frac{\sqrt{2}}{2}+\left(\sqrt{3}-2\right)^{0}$$

Express \sqrt{2}\times \frac{\sqrt{2}}{2} as a single fraction.

$$5-\frac{\sqrt{2}\sqrt{2}}{2}+\left(\sqrt{3}-2\right)^{0}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$5-\frac{2}{2}+\left(\sqrt{3}-2\right)^{0}$$

Divide 2 by 2 to get 1.

$$5-1+\left(\sqrt{3}-2\right)^{0}$$

Subtract 1 from 5 to get 4.

$$4+\left(\sqrt{3}-2\right)^{0}$$

Calculate \sqrt{3}-2 to the power of 0 and get 1.

$$4+1$$

Add 4 and 1 to get 5.

$$5$$