Question

To round a number to the nearest tenth, we must To reduce (or simplify) a radical, we must

Answer 1

For this we must observe the next place value to the right (the hundredths). If it is a 4 or less, we do not take into account the following digits to the right. If it is a 5 or greater, add a 1 to the digit in the tenths place, and then remove all digits to the right. For example,

`\begin{gathered} 85,14732\text{ }\Rightarrow85,4\text{ because the hundredths is a 4} \\ 34,68296\text{ }\Rightarrow34,7\text{ because the hundredthis is greater than 5} \end{gathered}`

For second question, to reduce a radical, we must write in the simplest form, so that:

* The index and exponent are prime to each other. For example,

`\sqrt[3]{x^2}\text{ }\Rightarrow\text{ the index (2) and the exponent (3) are primes in this case}`

*No factor can be extracted from the radicand. For example,

`\sqrt[]{20}=\sqrt[]{4\cdot5}=\sqrt[]{4}\cdot\sqrt[]{5}=2\sqrt[]{5}`

*The radicand has no fraction. For example,

`\sqrt[]{(5)/(4)}\Rightarrow\frac{\sqrt[]{5}}{\sqrt[]{4}}=\frac{\sqrt[]{5}}{2}`