Solve sqrt{18}-(sqrt{98}-2sqrt{75}+sqrt{3})

$$\sqrt { 18 } - ( \sqrt { 98 } - 2 \sqrt { 75 } + \sqrt { 3 } )$$

Evaluate

$$9\sqrt{3}-4\sqrt{2}\approx 9.931603019$$

Solution Steps

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$3\sqrt{2}-\left(\sqrt{98}-2\sqrt{75}+\sqrt{3}\right)$$

Factor 98=7^{2}\times 2. Rewrite the square root of the product \sqrt{7^{2}\times 2} as the product of square roots \sqrt{7^{2}}\sqrt{2}. Take the square root of 7^{2}.

$$3\sqrt{2}-\left(7\sqrt{2}-2\sqrt{75}+\sqrt{3}\right)$$

Factor 75=5^{2}\times 3. Rewrite the square root of the product \sqrt{5^{2}\times 3} as the product of square roots \sqrt{5^{2}}\sqrt{3}. Take the square root of 5^{2}.

$$3\sqrt{2}-\left(7\sqrt{2}-2\times 5\sqrt{3}+\sqrt{3}\right)$$

Multiply -2 and 5 to get -10.

$$3\sqrt{2}-\left(7\sqrt{2}-10\sqrt{3}+\sqrt{3}\right)$$

Combine -10\sqrt{3} and \sqrt{3} to get -9\sqrt{3}.

$$3\sqrt{2}-\left(7\sqrt{2}-9\sqrt{3}\right)$$

To find the opposite of 7\sqrt{2}-9\sqrt{3}, find the opposite of each term.

$$3\sqrt{2}-7\sqrt{2}-\left(-9\sqrt{3}\right)$$

Combine 3\sqrt{2} and -7\sqrt{2} to get -4\sqrt{2}.

$$-4\sqrt{2}-\left(-9\sqrt{3}\right)$$

The opposite of -9\sqrt{3} is 9\sqrt{3}.

$$-4\sqrt{2}+9\sqrt{3}$$