Question

Use a calculator to evaluate the expression. Round the results to the nearest hundredth. $$\frac{3 \pm 4 \sqrt{5}}{4}$$

Short answer

The expression evaluates to \(2.99\) and \(-1.49\) when rounded to the nearest hundredth.

Step-by-step solution

Solve The Square Root

The first step is to solve the square root in the expression, it is written as \( \sqrt{5} \). The square root of 5 is approximately \(2.23607\).

Multiply the result by 4

According to the order of operations (PEMDAS/BODMAS), multiplication should be done before addition or subtraction. Multiply the result of the square root of 5 from Step 1 by 4. This gives \(4*2.23607 = 8.94428\).

Evaluate the addition and subtraction separately

As the expression requires both addition and subtraction, calculate both of them separately. For addition, it is \(3 + 8.94428 = 11.94428 \) and for subtraction it is \(3 - 8.94428 = -5.94428\).

Divide the Results by 4

The numerator from step 3 should be divided by 4 to evaluate the fraction. For the addition, \(11.94428 / 4 = 2.98607\) and for the subtraction, \(-5.94428 / 4 = -1.48607\).

Round off to the Nearest Hundredth

Finally, round the answer from step 4 to the nearest hundredths place. The values of the expressions become \(2.99\) and \(-1.49\) respectively.