Solve (5sqrt{3}+7sqrt{2})(6sqrt{3}+4sqrt{2})

$$( 5 \sqrt { 3 } + 7 \sqrt { 2 } ) ( 6 \sqrt { 3 } + 4 \sqrt { 2 } )$$

Evaluate

$$62\sqrt{6}+146\approx 297.868364053$$

Solution Steps

Apply the distributive property by multiplying each term of 5\sqrt{3}+7\sqrt{2} by each term of 6\sqrt{3}+4\sqrt{2}.

$$30\left(\sqrt{3}\right)^{2}+20\sqrt{3}\sqrt{2}+42\sqrt{3}\sqrt{2}+28\left(\sqrt{2}\right)^{2}$$

The square of \sqrt{3} is 3.

$$30\times 3+20\sqrt{3}\sqrt{2}+42\sqrt{3}\sqrt{2}+28\left(\sqrt{2}\right)^{2}$$

Multiply 30 and 3 to get 90.

$$90+20\sqrt{3}\sqrt{2}+42\sqrt{3}\sqrt{2}+28\left(\sqrt{2}\right)^{2}$$

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

$$90+20\sqrt{6}+42\sqrt{3}\sqrt{2}+28\left(\sqrt{2}\right)^{2}$$

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

$$90+20\sqrt{6}+42\sqrt{6}+28\left(\sqrt{2}\right)^{2}$$

Combine 20\sqrt{6} and 42\sqrt{6} to get 62\sqrt{6}.

$$90+62\sqrt{6}+28\left(\sqrt{2}\right)^{2}$$

The square of \sqrt{2} is 2.

$$90+62\sqrt{6}+28\times 2$$

Multiply 28 and 2 to get 56.

$$90+62\sqrt{6}+56$$

Add 90 and 56 to get 146.

$$146+62\sqrt{6}$$

Factor

$$2 {(31 \sqrt{6} + 73)} = 297.868364053$$