Solve P=8+8sqrt{8}text{dan}Q=(sqrt{8}+sqrt{8})^2

$$P = 8 + 8 \sqrt { 8 } \text { dan } Q = ( \sqrt { 8 } + \sqrt { 8 } ) ^ { 2 }$$

Solve for P, Q

$$P=16\sqrt{2}+8\approx 30.627416998$$

$$Q=32$$

Solution Steps

Consider the first 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}.

$$P=8+8\times 2\sqrt{2}$$

Multiply 8 and 2 to get 16.

$$P=8+16\sqrt{2}$$

Consider the second 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}.

$$Q=\left(2\sqrt{2}+\sqrt{8}\right)^{2}$$

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}.

$$Q=\left(2\sqrt{2}+2\sqrt{2}\right)^{2}$$

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

$$Q=\left(4\sqrt{2}\right)^{2}$$

Expand \left(4\sqrt{2}\right)^{2}.

$$Q=4^{2}\left(\sqrt{2}\right)^{2}$$

Calculate 4 to the power of 2 and get 16.

$$Q=16\left(\sqrt{2}\right)^{2}$$

The square of \sqrt{2} is 2.

$$Q=16\times 2$$

Multiply 16 and 2 to get 32.

$$Q=32$$

The system is now solved.

$$P=8+16\sqrt{2} Q=32$$