Find the root and sImpllfy the expression. 625^(1)/(4)+8^(1)/(3) The radical Is square square 625^(1)/(4)+8^(1)/(3)=

To find the root and simplify the expression \(625^{\frac{1}{4}} + 8^{\frac{1}{3}}\), we need to evaluate each term separately.<br /><br />First, let's evaluate \(625^{\frac{1}{4}}\):<br />\[ 625^{\frac{1}{4}} = \sqrt[4]{625} \]<br /><br />We know that \(625 = 5^4\), so:<br />\[ \sqrt[4]{625} = \sqrt[4]{5^4} = 5 \]<br /><br />Next, let's evaluate \(8^{\frac{1}{3}}\):<br />\[ 8^{\frac{1}{3}} = \sqrt[3]{8} \]<br /><br />We know that \(8 = 2^3\), so:<br />\[ \sqrt[3]{8} = \sqrt[3]{2^3} = 2 \]<br /><br />Now, we add the two results together:<br />\[ 625^{\frac{1}{4}} + 8^{\frac{1}{3}} = 5 + 2 = 7 \]<br /><br />So, the simplified expression is:<br />\[ 625^{\frac{1}{4}} + 8^{\frac{1}{3}} = 7 \]<br /><br />The radical is \( \boxed{7} \).