Solve left|2*2+2*(-3)-1right|/sqrt{2^2+2^2}

$$\frac{ \left| 2 \times 2+2 \times (-3)-1 \right| }{ \sqrt{ { 2 }^{ 2 } + { 2 }^{ 2 } } }$$

Evaluate

$$\frac{3\sqrt{2}}{4}\approx 1.060660172$$

Solution Steps

Multiply 2 and 2 to get 4. Multiply 2 and -3 to get -6.

$$\frac{|4-6-1|}{\sqrt{2^{2}+2^{2}}}$$

Subtract 6 from 4 to get -2.

$$\frac{|-2-1|}{\sqrt{2^{2}+2^{2}}}$$

Subtract 1 from -2 to get -3.

$$\frac{|-3|}{\sqrt{2^{2}+2^{2}}}$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -3 is 3.

$$\frac{3}{\sqrt{2^{2}+2^{2}}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{3}{\sqrt{4+2^{2}}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{3}{\sqrt{4+4}}$$

Add 4 and 4 to get 8.

$$\frac{3}{\sqrt{8}}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$\frac{3}{2\sqrt{2}}$$

Rationalize the denominator of \frac{3}{2\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

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

The square of \sqrt{2} is 2.

$$\frac{3\sqrt{2}}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$\frac{3\sqrt{2}}{4}$$