A-level Mathematics/OCR/C1/Indices and Surds/Problems

< A-level Mathematics < OCR < C1 < Indices and Surds

Feel free to add more problems as long as you provide the solutions

Indices

Simplify the Indices.

$x^{2}x^{3}$
$x^{3}x^{-2}$
${\frac {x^{5}}{x^{2}}}$
$x^{-4}$
$\left(x^{3}\right)^{4}$
$\left(xy\right)^{2}$
$\left({\frac {y}{b}}\right)^{3}$
$x^{\frac {2}{3}}$
${\frac {x^{2}x^{4}}{\left(x^{2}\right)^{2}}}$
$x^{5}x^{-5}$

Surds

Simplify the following Surds.

${\sqrt {9}}$
${\sqrt {25}}$
${\sqrt {45}}$
${\sqrt {63}}$
${\sqrt {100}}$
${\sqrt {48}}$
${\sqrt {98}}$
${\sqrt {75}}$
${\sqrt {32}}$
${\sqrt {320}}$
${\sqrt {256}}$
${\sqrt {\frac {9}{36}}}$
${\sqrt[{3}]{\frac {27}{125}}}$
${\sqrt {\frac {162}{200}}}$
${\sqrt {\frac {75}{3}}}$
${\sqrt {\frac {112}{72}}}$

Rationalize the Denominator

${\frac {2}{\sqrt {4}}}$
${\frac {8}{4+{\sqrt {26}}}}$
${\frac {12}{12-{\sqrt {76}}}}$
${\frac {3}{3-{\sqrt {65}}}}$
${\frac {9}{9+{\sqrt {9}}}}$
${\frac {a^{2}}{a+{\sqrt {a}}}}$

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