Solve 4sqrt{6}(sqrt{7}-sqrt{6})

$$4 \sqrt { 6 } ( \sqrt { 7 } - \sqrt { 6 } )$$

Evaluate

$$4\left(\sqrt{42}-6\right)\approx 1.922962794$$

Solution Steps

Use the distributive property to multiply 4\sqrt{6} by \sqrt{7}-\sqrt{6}.

$$4\sqrt{6}\sqrt{7}-4\left(\sqrt{6}\right)^{2}$$

To multiply \sqrt{6} and \sqrt{7}, multiply the numbers under the square root.

$$4\sqrt{42}-4\left(\sqrt{6}\right)^{2}$$

The square of \sqrt{6} is 6.

$$4\sqrt{42}-4\times 6$$

Multiply -4 and 6 to get -24.

$$4\sqrt{42}-24$$