Solve B=(sqrt{5}+sqrt{2})(sqrt{10}-1)

$$B = ( \sqrt { 5 } + \sqrt { 2 } ) ( \sqrt { 10 } - 1 )$$

Solve for B

$$B=\sqrt{5}+4\sqrt{2}\approx 7.892922227$$

Steps for Solving Linear Equation

Apply the distributive property by multiplying each term of \sqrt{5}+\sqrt{2} by each term of \sqrt{10}-1.

$$B=\sqrt{5}\sqrt{10}-\sqrt{5}+\sqrt{2}\sqrt{10}-\sqrt{2}$$

Factor 10=5\times 2. Rewrite the square root of the product \sqrt{5\times 2} as the product of square roots \sqrt{5}\sqrt{2}.

$$B=\sqrt{5}\sqrt{5}\sqrt{2}-\sqrt{5}+\sqrt{2}\sqrt{10}-\sqrt{2}$$

Multiply \sqrt{5} and \sqrt{5} to get 5.

$$B=5\sqrt{2}-\sqrt{5}+\sqrt{2}\sqrt{10}-\sqrt{2}$$

Factor 10=2\times 5. Rewrite the square root of the product \sqrt{2\times 5} as the product of square roots \sqrt{2}\sqrt{5}.

$$B=5\sqrt{2}-\sqrt{5}+\sqrt{2}\sqrt{2}\sqrt{5}-\sqrt{2}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$B=5\sqrt{2}-\sqrt{5}+2\sqrt{5}-\sqrt{2}$$

Combine -\sqrt{5} and 2\sqrt{5} to get \sqrt{5}.

$$B=5\sqrt{2}+\sqrt{5}-\sqrt{2}$$

Combine 5\sqrt{2} and -\sqrt{2} to get 4\sqrt{2}.

$$B=4\sqrt{2}+\sqrt{5}$$

Assign B

$$B≔\sqrt{5}+4\sqrt{2}$$