Solve -42/1+sqrt{15}

$$\frac { - 42 } { 1 + \sqrt { 15 } }$$

Evaluate

$$3-3\sqrt{15}\approx -8.618950039$$

Solution Steps

Rationalize the denominator of \frac{-42}{1+\sqrt{15}} by multiplying numerator and denominator by 1-\sqrt{15}.

$$\frac{-42\left(1-\sqrt{15}\right)}{\left(1+\sqrt{15}\right)\left(1-\sqrt{15}\right)}$$

Consider \left(1+\sqrt{15}\right)\left(1-\sqrt{15}\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{-42\left(1-\sqrt{15}\right)}{1^{2}-\left(\sqrt{15}\right)^{2}}$$

Square 1. Square \sqrt{15}.

$$\frac{-42\left(1-\sqrt{15}\right)}{1-15}$$

Subtract 15 from 1 to get -14.

$$\frac{-42\left(1-\sqrt{15}\right)}{-14}$$

Divide -42\left(1-\sqrt{15}\right) by -14 to get 3\left(1-\sqrt{15}\right).

$$3\left(1-\sqrt{15}\right)$$

Use the distributive property to multiply 3 by 1-\sqrt{15}.

$$3-3\sqrt{15}$$