Solve A=3sqrt{10}-5,quadB=2sqrt{10-2},quadC=3sqrt{3-2}

$$A = 3 \sqrt { 10 } - 5 , \quad B = 2 \sqrt { 10 - 2 } , \quad C = 3 \sqrt { 3 - 2 }$$

Solve for A, B, C

$$A=3\sqrt{10}-5\approx 4.486832981$$

$$B=4\sqrt{2}\approx 5.656854249$$

$$C=3$$

Solution Steps

Consider the second equation. Subtract 2 from 10 to get 8.

$$B=2\sqrt{8}$$

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}.

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

Multiply 2 and 2 to get 4.

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

Consider the third equation. Subtract 2 from 3 to get 1.

$$C=3\sqrt{1}$$

Calculate the square root of 1 and get 1.

$$C=3\times 1$$

Multiply 3 and 1 to get 3.

$$C=3$$

The system is now solved.

$$A=3\sqrt{10}-5 B=4\sqrt{2} C=3$$