Question
Simplify the following:$\frac{\sqrt[4]{1250}}{\sqrt[4]{2}}$
✓
Answer
We know that $\frac{\sqrt[\text{n}]{\text{a}}}{{\sqrt[\text{n}]{\text{b}}}}=\sqrt[\text{n}]{\frac{\text{a}}{\text{b}}}.$
We will use this property to simplify the expression $\frac{\sqrt[4]{1250}}{\sqrt[4]{2}}.$
$\therefore\ \frac{\sqrt[4]{1250}}{\sqrt[4]{2}}=\sqrt[4]{625}$
$=\sqrt[4]{5^4}$
$=(5^4)^\frac{1}{4}$
$=(5)^1$
$=5$ Hence the value of the given expression is $5.$
We will use this property to simplify the expression $\frac{\sqrt[4]{1250}}{\sqrt[4]{2}}.$
$\therefore\ \frac{\sqrt[4]{1250}}{\sqrt[4]{2}}=\sqrt[4]{625}$
$=\sqrt[4]{5^4}$
$=(5^4)^\frac{1}{4}$
$=(5)^1$
$=5$ Hence the value of the given expression is $5.$
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