Solve (4sqrt{2}+8sqrt{5})(9sqrt{2}+4sqrt{5})

$$( 4 \sqrt { 2 } + 8 \sqrt { 5 } ) ( 9 \sqrt { 2 } + 4 \sqrt { 5 } )$$

Evaluate

$$88\sqrt{10}+232\approx 510.280434095$$

Solution Steps

Apply the distributive property by multiplying each term of 4\sqrt{2}+8\sqrt{5} by each term of 9\sqrt{2}+4\sqrt{5}.

$$36\left(\sqrt{2}\right)^{2}+16\sqrt{2}\sqrt{5}+72\sqrt{5}\sqrt{2}+32\left(\sqrt{5}\right)^{2}$$

The square of \sqrt{2} is 2.

$$36\times 2+16\sqrt{2}\sqrt{5}+72\sqrt{5}\sqrt{2}+32\left(\sqrt{5}\right)^{2}$$

Multiply 36 and 2 to get 72.

$$72+16\sqrt{2}\sqrt{5}+72\sqrt{5}\sqrt{2}+32\left(\sqrt{5}\right)^{2}$$

To multiply \sqrt{2} and \sqrt{5}, multiply the numbers under the square root.

$$72+16\sqrt{10}+72\sqrt{5}\sqrt{2}+32\left(\sqrt{5}\right)^{2}$$

To multiply \sqrt{5} and \sqrt{2}, multiply the numbers under the square root.

$$72+16\sqrt{10}+72\sqrt{10}+32\left(\sqrt{5}\right)^{2}$$

Combine 16\sqrt{10} and 72\sqrt{10} to get 88\sqrt{10}.

$$72+88\sqrt{10}+32\left(\sqrt{5}\right)^{2}$$

The square of \sqrt{5} is 5.

$$72+88\sqrt{10}+32\times 5$$

Multiply 32 and 5 to get 160.

$$72+88\sqrt{10}+160$$

Add 72 and 160 to get 232.

$$232+88\sqrt{10}$$

Factor

$$8 {(11 \sqrt{10} + 29)} = 510.280434095$$