Surds are square roots which can’t be reduced to rational numbers. Some can be simplified using various rules or by rationalising the denominator.

Which of the following is a surd?

\[\sqrt {64}\]

\[\sqrt {18}\]

\[\sqrt {100}\]

Simplify \(\sqrt {75}\)

\[5\sqrt 3\]

\[5\sqrt {15}\]

\[15\sqrt 5\]

Simplify \(\sqrt 6 \times \sqrt 8\)

\[\sqrt {48}\]

\[2\sqrt {12}\]

\[4\sqrt 3\]

Simplify \(\frac{{\sqrt 5 }}{{\sqrt {90} }}\) giving your answer with a rational denominator.

\[\sqrt {\frac{5}{{90}}}\]

\[\frac{1}{{3\sqrt 2 }}\]

\[\frac{{\sqrt 2 }}{6}\]

Simplify \(\sqrt {0.49}\)

\[\sqrt {\frac{{49}}{{100}}}\]

\[0.7\]

\[0.07\]

Simplify \(\sqrt 2 + \sqrt {18}\)

\[4\sqrt 2\]

\[3\sqrt 2\]

\[6\]

Rationalise the denominator of:\(\frac{5}{4-\sqrt{6}}\)

\[2+\sqrt{3}\]

\[\frac{4+\sqrt{6}}{2}\]

\[-\frac{4+\sqrt{6}}{2}\]

Solve the equation \(2{x^2} + 3 = 57\)

\[\sqrt {30}\]

\[\sqrt {27}\]

\[3\sqrt 3\]

Calculate the missing side, leaving your answer as a surd in its simplest form.

\[3\sqrt 2 m\]

\[\sqrt {18} m\]

\[\sqrt {82} m\]

Rationalise the denominator of \(\frac{4}{7-3\sqrt{2}}\).

\[\frac{4}{4\sqrt{2}}\]

\[\frac{28+12\sqrt{2}}{31}\]

\[\frac{28-12\sqrt{2}}{67-42\sqrt{2}}\]