Solve (sqrt{28}-2sqrt{3}+sqrt{7})*sqrt{7}+sqrt{8}

$$( \sqrt { 28 } - 2 \sqrt { 3 } + \sqrt { 7 } ) \times \sqrt { 7 } + \sqrt { 8 }$$

Evaluate

$$2\sqrt{2}+21-2\sqrt{21}\approx 14.663275735$$

Solution Steps

Factor 28=2^{2}\times 7. Rewrite the square root of the product \sqrt{2^{2}\times 7} as the product of square roots \sqrt{2^{2}}\sqrt{7}. Take the square root of 2^{2}.

$$\left(2\sqrt{7}-2\sqrt{3}+\sqrt{7}\right)\sqrt{7}+\sqrt{8}$$

Combine 2\sqrt{7} and \sqrt{7} to get 3\sqrt{7}.

$$\left(3\sqrt{7}-2\sqrt{3}\right)\sqrt{7}+\sqrt{8}$$

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

$$3\left(\sqrt{7}\right)^{2}-2\sqrt{3}\sqrt{7}+\sqrt{8}$$

The square of \sqrt{7} is 7.

$$3\times 7-2\sqrt{3}\sqrt{7}+\sqrt{8}$$

Multiply 3 and 7 to get 21.

$$21-2\sqrt{3}\sqrt{7}+\sqrt{8}$$

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

$$21-2\sqrt{21}+\sqrt{8}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$21-2\sqrt{21}+2\sqrt{2}$$