Question

Express each number as a mixed radical in simplest form.a) 4√18 − 2√63 + √175 + 5√98

Answer 1

Let's simplify the expression:

`\begin{gathered} 4\sqrt[]{18}-2\sqrt[]{63}+\sqrt[]{175}+5\sqrt[]{98}=4\sqrt[]{9\cdot2}-2\sqrt[]{9\cdot7}+\sqrt[]{25\cdot7}+5\sqrt[]{49\cdot2} \\ =4\cdot3\sqrt[]{2}-2\cdot3\sqrt[]{7}+5\sqrt[]{7}+5\cdot7\sqrt[]{2} \\ =12\sqrt[]{2}-6\sqrt[]{7}+5\sqrt[]{7}+35\sqrt[]{2} \\ =47\sqrt[]{2}-\sqrt[]{7} \end{gathered}`

Therefore the simplified form is:

`47\sqrt[]{2}-\sqrt[]{7}`