Solve sqrt[4]{4}+sqrt{3}-12sqrt[3]{64}

$$\sqrt[ 4 ] { 4 } + \sqrt { 3 } - 12 \sqrt[ 3 ] { 64 }$$

Evaluate

$$\sqrt{2}+\sqrt{3}-48\approx -44.85373563$$

Solution Steps

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

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

Insert the obtained value back in the expression.

$$\sqrt{2}+\sqrt{3}-12\sqrt[3]{64}$$

Calculate \sqrt[3]{64} and get 4.

$$\sqrt{2}+\sqrt{3}-12\times 4$$

Multiply -12 and 4 to get -48.

$$\sqrt{2}+\sqrt{3}-48$$