Solve sqrt{25}-4sqrt{50}+sqrt{100}

$$\sqrt{ 25 } -4 \sqrt{ 50 } + \sqrt{ 100 }$$

Evaluate

$$15-20\sqrt{2}\approx -13.284271247$$

Solution Steps

Calculate the square root of 25 and get 5.

$$5-4\sqrt{50}+\sqrt{100}$$

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}.

$$5-4\times 5\sqrt{2}+\sqrt{100}$$

Multiply -4 and 5 to get -20.

$$5-20\sqrt{2}+\sqrt{100}$$

Calculate the square root of 100 and get 10.

$$5-20\sqrt{2}+10$$

Add 5 and 10 to get 15.

$$15-20\sqrt{2}$$