Solve B=sqrt{2}+sqrt{8}-sqrt{32}

$$B = \sqrt { 2 } + \sqrt { 8 } - \sqrt { 32 }$$

Solve for B

$$B=-\sqrt{2}\approx -1.414213562$$

Steps for Solving Linear Equation

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}.

$$B=\sqrt{2}+2\sqrt{2}-\sqrt{32}$$

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

$$B=3\sqrt{2}-\sqrt{32}$$

Factor 32=4^{2}\times 2. Rewrite the square root of the product \sqrt{4^{2}\times 2} as the product of square roots \sqrt{4^{2}}\sqrt{2}. Take the square root of 4^{2}.

$$B=3\sqrt{2}-4\sqrt{2}$$

Combine 3\sqrt{2} and -4\sqrt{2} to get -\sqrt{2}.

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

Assign B

$$B≔-\sqrt{2}$$