Solve (sqrt{45}-sqrt{36})(sqrt{45}+sqrt{36})

$$( \sqrt { 45 } - \sqrt { 36 } ) ( \sqrt { 45 } + \sqrt { 36 } )$$

Evaluate

$$9$$

Solution Steps

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

$$\left(\sqrt{45}\right)^{2}-\left(\sqrt{36}\right)^{2}$$

The square of \sqrt{45} is 45.

$$45-\left(\sqrt{36}\right)^{2}$$

The square of \sqrt{36} is 36.

$$45-36$$

Subtract 36 from 45 to get 9.

$$9$$

Factor

$$3^{2}$$