Solve (2sqrt{7}+sqrt{12})*(sqrt{12}*sqrt{7})-sqrt{84}=

$$( 2 \sqrt { 7 } + \sqrt { 12 } ) \cdot ( \sqrt { 12 } \cdot \sqrt { 7 } ) - \sqrt { 84 } =$$

Evaluate

$$12\sqrt{7}+28\sqrt{3}-2\sqrt{21}\approx 71.081286955$$

Solution Steps

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$\left(2\sqrt{7}+2\sqrt{3}\right)\sqrt{12}\sqrt{7}-\sqrt{84}$$

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$\left(2\sqrt{7}+2\sqrt{3}\right)\times 2\sqrt{3}\sqrt{7}-\sqrt{84}$$

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

$$\left(2\sqrt{7}+2\sqrt{3}\right)\times 2\sqrt{21}-\sqrt{84}$$

Use the distributive property to multiply 2\sqrt{7}+2\sqrt{3} by 2.

$$\left(4\sqrt{7}+4\sqrt{3}\right)\sqrt{21}-\sqrt{84}$$

Use the distributive property to multiply 4\sqrt{7}+4\sqrt{3} by \sqrt{21}.

$$4\sqrt{7}\sqrt{21}+4\sqrt{3}\sqrt{21}-\sqrt{84}$$

Factor 21=7\times 3. Rewrite the square root of the product \sqrt{7\times 3} as the product of square roots \sqrt{7}\sqrt{3}.

$$4\sqrt{7}\sqrt{7}\sqrt{3}+4\sqrt{3}\sqrt{21}-\sqrt{84}$$

Multiply \sqrt{7} and \sqrt{7} to get 7.

$$4\times 7\sqrt{3}+4\sqrt{3}\sqrt{21}-\sqrt{84}$$

Multiply 4 and 7 to get 28.

$$28\sqrt{3}+4\sqrt{3}\sqrt{21}-\sqrt{84}$$

Factor 21=3\times 7. Rewrite the square root of the product \sqrt{3\times 7} as the product of square roots \sqrt{3}\sqrt{7}.

$$28\sqrt{3}+4\sqrt{3}\sqrt{3}\sqrt{7}-\sqrt{84}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$28\sqrt{3}+4\times 3\sqrt{7}-\sqrt{84}$$

Multiply 4 and 3 to get 12.

$$28\sqrt{3}+12\sqrt{7}-\sqrt{84}$$

Factor 84=2^{2}\times 21. Rewrite the square root of the product \sqrt{2^{2}\times 21} as the product of square roots \sqrt{2^{2}}\sqrt{21}. Take the square root of 2^{2}.

$$28\sqrt{3}+12\sqrt{7}-2\sqrt{21}$$