Solve sqrt{125}-sqrt{45}+sqrt[4]{25}-3sqrt{5}

$$\sqrt{ 125 } - \sqrt{ 45 } + \sqrt[ 4 ]{ 25 } -3 \sqrt{ 5 }$$

Evaluate

$$0$$

Solution Steps

Factor 125=5^{2}\times 5. Rewrite the square root of the product \sqrt{5^{2}\times 5} as the product of square roots \sqrt{5^{2}}\sqrt{5}. Take the square root of 5^{2}.

$$5\sqrt{5}-\sqrt{45}+\sqrt[4]{25}-3\sqrt{5}$$

Factor 45=3^{2}\times 5. Rewrite the square root of the product \sqrt{3^{2}\times 5} as the product of square roots \sqrt{3^{2}}\sqrt{5}. Take the square root of 3^{2}.

$$5\sqrt{5}-3\sqrt{5}+\sqrt[4]{25}-3\sqrt{5}$$

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

$$2\sqrt{5}+\sqrt[4]{25}-3\sqrt{5}$$

Rewrite \sqrt[4]{25} as \sqrt[4]{5^{2}}. Convert from radical to exponential form and cancel out 2 in the exponent. Convert back to radical form.

$$\sqrt[4]{25}=\sqrt[4]{5^{2}}=5^{\frac{2}{4}}=5^{\frac{1}{2}}=\sqrt{5}$$

Insert the obtained value back in the expression.

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

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

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

Combine 3\sqrt{5} and -3\sqrt{5} to get 0.

$$0$$

Factor

$$0$$