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Radical Expressions and Equations

Combine your skills of working with exponents and manipulating expressions for radical glory.

Simplifying Radical Expressions

Evaluate \( \sqrt{ 40 ^2 + 42 ^2}\).

The value of \[\sqrt{\frac{5}{72}} \left(\sqrt{\frac{9}{40}}-\sqrt{\frac{8}{45}}\right)\] can be expressed as \(\frac{1}{a}\). What is \(a\)?

Evaluate

\[ \sqrt{2} - \frac{1}{ \sqrt{2} - \dfrac{1}{ \sqrt{2} - \dfrac{1}{\sqrt{2}-1} } }. \]

Evaluate

\[ \left( 4\sqrt{3} +7 \right)^{2016} \left( 4\sqrt{3} -7 \right)^{2016}. \]

What is the value of

\[ \sqrt{ 24 } \times \sqrt{3} \times \sqrt{ 8 } ? \]

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