Simplify.
$\frac{6-\sqrt{25}}{4}=$
$\square$
Use a calculator to estimate the value. Round to the nearest hundredth.
$\frac{-2-\sqrt{15}}{2} \approx$
$\square$
Answer (1)
Simplify the first expression by evaluating the square root and performing the subtraction and division: 4 6 − 25 = 4 6 − 5 = 4 1 .
Estimate the value of the second expression using a calculator: 2 − 2 − 15 ≈ − 2.936491673 .
Round the result to the nearest hundredth: − 2.936491673 ≈ − 2.94 .
The simplified expression is 4 1 and the estimated value rounded to the nearest hundredth is − 2.94 .
Explanation
Understanding the Problem We are asked to simplify the expression 4 6 − 25 and to estimate the value of 2 − 2 − 15 rounded to the nearest hundredth.
Simplifying the Square Root First, let's simplify the expression 4 6 − 25 . We know that 25 = 5 , so we can substitute this value into the expression: 4 6 − 5
Performing Subtraction Now, we perform the subtraction in the numerator: 6 − 5 = 1 So the expression becomes: 4 1
Simplified Expression Thus, the simplified expression is 4 1 .
Estimating the Value Next, we need to estimate the value of 2 − 2 − 15 and round to the nearest hundredth. Using a calculator, we find that 2 − 2 − 15 ≈ − 2.936491673
Rounding to Nearest Hundredth Rounding this value to the nearest hundredth, we get − 2.94 .
Final Answer Therefore, the simplified expression is 4 1 and the estimated value of the second expression rounded to the nearest hundredth is − 2.94 .
Examples
Imagine you're baking a cake and need to adjust a recipe. Simplifying fractions helps you measure ingredients accurately, like reducing 4 6 − 25 to 4 1 for precise measurements. Estimating values, such as 2 − 2 − 15 ≈ − 2.94 , is useful for quickly approximating quantities when exact measurements aren't crucial. These skills ensure your cake turns out perfectly!
