Question

1. use your calculator to evaluate each expression. express answers to two decimals.

a) ( 125^{1/3} )
d) ( 16^{3/4} )
b) ( sqrt3{-1953.125} )
e) ( 10^{-1/2} )
c) ( sqrt3{-180} )
f) ( sqrt5{1.9} )

Explanation:

Step1: Evaluate \(125^{1/3}\)

The cube root of 125. Since \(5^3 = 125\), so \(125^{1/3}=5.00\) (to two decimals).

Step2: Evaluate \(\sqrt[3]{-1953.125}\)

We know that \((-12.5)^3=-1953.125\), so \(\sqrt[3]{-1953.125}=-12.50\) (to two decimals).

Step3: Evaluate \(\sqrt[3]{-180}\)

Using a calculator, \(\sqrt[3]{-180}\approx -5.646\), rounded to two decimals is \(-5.65\).

Step4: Evaluate \(16^{3/4}\)

First, \(16^{1/4}=2\) (since \(2^4 = 16\)), then \(2^3 = 8\), so \(16^{3/4}=8.00\) (to two decimals).

Step5: Evaluate \(10^{-1/3}\)

This is \(\frac{1}{10^{1/3}}\). \(10^{1/3}\approx2.154\), so \(\frac{1}{2.154}\approx0.46\) (to two decimals).

Step6: Evaluate \(\sqrt[5]{1.9}\)

Using a calculator, \(\sqrt[5]{1.9}\approx1.14\) (to two decimals).

Answer:

a) \(5.00\)
b) \(-12.50\)
c) \(-5.65\)
d) \(8.00\)
e) \(0.46\)
f) \(1.14\)