1.06 Irrational numbers
State which of the following are rational or irrational:
\sqrt{25}
\sqrt{361}
\sqrt{33}
\sqrt[3]{64}
\sqrt[3]{47}
\sqrt[3]{125}
\sqrt[3]{1000}
\sqrt[3]{1729}
Evaluate the following, rounding your answers to two decimal places where necessary:
\sqrt{25}
\sqrt[3]{64}
\sqrt{33}
\sqrt[3]{26}
\sqrt{121}
\sqrt[3]{216}
\sqrt{83}
\sqrt[3]{52}
Is \sqrt{15} an integer?
Determine whether each of the following numbers is a surd:
\sqrt{2}
\sqrt{1}
\sqrt{50}
\sqrt[3]{27}
\sqrt[3]{9}
\sqrt[3]{8}
\sqrt{80}
\sqrt{144}
What is the largest square number that divides exactly into\, 108?
Consider\sqrt{290} and answer the following questions:
Is \sqrt{290} an exact value?
A calculator states that \sqrt{290} is 17.029386366. Is this still exact?
Are the following expressions written in their simplest surd form?:
\sqrt{17}
\sqrt{14}
\sqrt{50}
5 \sqrt{50}
7 \sqrt{125}
11 \sqrt{21}
\sqrt{63}
\sqrt{112}
Simplify the following:
\sqrt{180}
\sqrt{125}
3 \sqrt{54}
7 \sqrt{32}
6 \sqrt{100}.
\sqrt{ 25 \times 6}
\dfrac{1}{2} \sqrt[3]{ 8 \times 6}.
\sqrt[3]{ 24 \times 9}.
Simplify the following:
\dfrac{1}{\sqrt{25}}
\dfrac{16}{\sqrt{16}}
\dfrac{\sqrt{64}}{8}
\dfrac{36}{\sqrt[3]{216}}
Write the expression 3 \sqrt{5} as a single surd.
Consider the equation x \sqrt{8} = \sqrt{648}. Find the value of the pronumeral x.
Consider the surd \sqrt{54}:
Simplify the surd.
Evaluate the surd to two decimal places.
Simplify the following:
\sqrt{100}
\sqrt{170}
\sqrt{64} \times \sqrt{1}
\sqrt[3]{64}