Solve (sqrt{7}+sqrt{3})(sqrt{7}+4sqrt{3})

$$( \sqrt { 7 } + \sqrt { 3 } ) ( \sqrt { 7 } + 4 \sqrt { 3 } )$$

Evaluate

$$5\sqrt{21}+19\approx 41.912878475$$

Solution Steps

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

$$\left(\sqrt{7}\right)^{2}+4\sqrt{7}\sqrt{3}+\sqrt{3}\sqrt{7}+4\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{7} is 7.

$$7+4\sqrt{7}\sqrt{3}+\sqrt{3}\sqrt{7}+4\left(\sqrt{3}\right)^{2}$$

To multiply \sqrt{7} and \sqrt{3}, multiply the numbers under the square root.

$$7+4\sqrt{21}+\sqrt{3}\sqrt{7}+4\left(\sqrt{3}\right)^{2}$$

To multiply \sqrt{3} and \sqrt{7}, multiply the numbers under the square root.

$$7+4\sqrt{21}+\sqrt{21}+4\left(\sqrt{3}\right)^{2}$$

Combine 4\sqrt{21} and \sqrt{21} to get 5\sqrt{21}.

$$7+5\sqrt{21}+4\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{3} is 3.

$$7+5\sqrt{21}+4\times 3$$

Multiply 4 and 3 to get 12.

$$7+5\sqrt{21}+12$$

Add 7 and 12 to get 19.

$$19+5\sqrt{21}$$