Solve 5-1-2sqrt{5-1}+sqrt{5^2+20-5}-4-2sqrt{9}

$$5 - 1 - 2 \sqrt { 5 - 1 } + \sqrt { 5 ^ { 2 } + 20 - 5 } - 4 - 2 \sqrt { 9 }$$

Evaluate

$$2\left(\sqrt{10}-5\right)\approx -3.67544468$$

Solution Steps

Subtract 1 from 5 to get 4.

$$4-2\sqrt{5-1}+\sqrt{5^{2}+20-5}-4-2\sqrt{9}$$

Subtract 1 from 5 to get 4.

$$4-2\sqrt{4}+\sqrt{5^{2}+20-5}-4-2\sqrt{9}$$

Calculate the square root of 4 and get 2.

$$4-2\times 2+\sqrt{5^{2}+20-5}-4-2\sqrt{9}$$

Multiply 2 and 2 to get 4.

$$4-4+\sqrt{5^{2}+20-5}-4-2\sqrt{9}$$

Subtract 4 from 4 to get 0.

$$0+\sqrt{5^{2}+20-5}-4-2\sqrt{9}$$

Calculate 5 to the power of 2 and get 25.

$$0+\sqrt{25+20-5}-4-2\sqrt{9}$$

Add 25 and 20 to get 45.

$$0+\sqrt{45-5}-4-2\sqrt{9}$$

Subtract 5 from 45 to get 40.

$$0+\sqrt{40}-4-2\sqrt{9}$$

Factor 40=2^{2}\times 10. Rewrite the square root of the product \sqrt{2^{2}\times 10} as the product of square roots \sqrt{2^{2}}\sqrt{10}. Take the square root of 2^{2}.

$$0+2\sqrt{10}-4-2\sqrt{9}$$

Subtract 4 from 0 to get -4.

$$-4+2\sqrt{10}-2\sqrt{9}$$

Calculate the square root of 9 and get 3.

$$-4+2\sqrt{10}-2\times 3$$

Multiply -2 and 3 to get -6.

$$-4+2\sqrt{10}-6$$

Subtract 6 from -4 to get -10.

$$-10+2\sqrt{10}$$