Solve (1+3sqrt{2}-(4-sqrt{50})

$$(1+3 \sqrt{ 2 } -(4- \sqrt{ 50 } )$$

Evaluate

$$8\sqrt{2}-3\approx 8.313708499$$

Solution Steps

Factor 50=5^{2}\times 2. Rewrite the square root of the product \sqrt{5^{2}\times 2} as the product of square roots \sqrt{5^{2}}\sqrt{2}. Take the square root of 5^{2}.

$$1+3\sqrt{2}-\left(4-5\sqrt{2}\right)$$

To find the opposite of 4-5\sqrt{2}, find the opposite of each term.

$$1+3\sqrt{2}-4-\left(-5\sqrt{2}\right)$$

Subtract 4 from 1 to get -3.

$$-3+3\sqrt{2}-\left(-5\sqrt{2}\right)$$

The opposite of -5\sqrt{2} is 5\sqrt{2}.

$$-3+3\sqrt{2}+5\sqrt{2}$$

Combine 3\sqrt{2} and 5\sqrt{2} to get 8\sqrt{2}.

$$-3+8\sqrt{2}$$