Question

7 fill in the blank 0.5 points simplify, if necessary round to the nearest hundredth √12 type your answer...

Explanation:

Step1: Simplify the square root

We know that \( \sqrt{12} = \sqrt{4\times3} \). By the property of square roots \( \sqrt{ab}=\sqrt{a}\times\sqrt{b} \) (where \( a = 4 \) and \( b=3 \)), we get \( \sqrt{4\times3}=\sqrt{4}\times\sqrt{3} \). Since \( \sqrt{4} = 2 \), this simplifies to \( 2\sqrt{3} \).

Step2: Calculate the decimal approximation

We know that \( \sqrt{3}\approx1.732 \). So, \( 2\sqrt{3}=2\times1.732 = 3.464 \).

Step3: Round to the nearest hundredth

To round \( 3.464 \) to the nearest hundredth, we look at the thousandths place, which is \( 4 \). Since \( 4<5 \), we keep the hundredths place as it is. So, \( 3.464\approx3.46 \).

Answer:

\( 3.46 \) (or \( 2\sqrt{3} \) if exact form is preferred, but the problem says to round to the nearest hundredth so \( 3.46 \) is appropriate)