Solve (5sqrt{2}-2sqrt{3})sqrt{3}

$$(5 \sqrt{ 2 } -2 \sqrt{ 3 } ) \sqrt{ 3 }$$

Evaluate

$$5\sqrt{6}-6\approx 6.247448714$$

Solution Steps

Use the distributive property to multiply 5\sqrt{2}-2\sqrt{3} by \sqrt{3}.

$$5\sqrt{2}\sqrt{3}-2\left(\sqrt{3}\right)^{2}$$

To multiply \sqrt{2} and \sqrt{3}, multiply the numbers under the square root.

$$5\sqrt{6}-2\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{3} is 3.

$$5\sqrt{6}-2\times 3$$

Multiply -2 and 3 to get -6.

$$5\sqrt{6}-6$$