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

$$\frac { 1 ^ { 2 } - 9 } { \sqrt { 2 ( 1 ) + 3 } }$$

Evaluate

$$-\frac{8\sqrt{5}}{5}\approx -3.577708764$$

Solution Steps

Calculate 1 to the power of 2 and get 1.

$$\frac{1-9}{\sqrt{2\times 1+3}}$$

Subtract 9 from 1 to get -8.

$$\frac{-8}{\sqrt{2\times 1+3}}$$

Multiply 2 and 1 to get 2.

$$\frac{-8}{\sqrt{2+3}}$$

Add 2 and 3 to get 5.

$$\frac{-8}{\sqrt{5}}$$

Rationalize the denominator of \frac{-8}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{-8\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{-8\sqrt{5}}{5}$$