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

These are the solutions to Indices and Surd Problems.

Indices

 * 1) $$x^5$$
 * 2) $$x$$
 * 3) $$x^3$$
 * 4) $$\frac{1}{x^4}$$
 * 5) $$x^{12}$$
 * 6) $$x^2y^2$$
 * 7) $$\frac{y^3}{b^3}$$
 * 8) $$\sqrt[3]{x^2}$$
 * 9) $$x^2$$
 * 10) $$1$$

Surds

 * 1) $$\sqrt{9} = 3$$
 * 2) $$\sqrt{25} = 5$$
 * 3) $$\sqrt{45} = \sqrt{9}\sqrt{5} = 3\sqrt{5}$$
 * 4) $$3\sqrt{7}$$
 * 5) $$\sqrt{100} = 10$$
 * 6) $$4\sqrt{3}$$
 * 7) $$7\sqrt{2}$$
 * 8) $$5\sqrt{3}$$
 * 9) $$4\sqrt{2}$$
 * 10) $$8\sqrt{5}$$
 * 11) $$16$$
 * 12) $$\frac{1}{2}$$
 * 13) $$\sqrt[3]{\frac{27}{125}}$$ = $$\frac{27^\frac{1}{3}}{125^\frac{1}{3}}$$ = $$\frac{3}{5}$$ (Note: $$x^\frac{1}{3} \times x^\frac{1}{3} \times x^\frac{1}{3}=x$$)
 * 14) $$\sqrt{\frac{162}{200}}$$ = $$\frac{\sqrt{162}}{\sqrt{200}}$$ = $$\frac{\sqrt{81}\times\sqrt{2}}{\sqrt{100}\times\sqrt{2}}$$ = $$\frac{9\sqrt{2}}{10\sqrt{2}}$$ = $$\frac{9}{10}$$
 * 15) $$5$$
 * 16) $$\frac{\sqrt{14}}{3}$$
 * 17) $$1$$ (denominator is already rational)
 * 18) $$- \frac{32 - 8\sqrt{26}}{10}$$
 * 19) $$\frac{144 + 24\sqrt{19}}{68}$$
 * 20) $$\frac{9 + 3\sqrt{65}}{-56}$$
 * 21) $$\frac{3}{4}$$
 * 22) $$\frac{{a^2}-a\sqrt{a}} {a-1}$$

Indices and Surds/Solutions