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

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

Indices

Simplify the Indices.

1. $x^2{x}^3$
2. $x^3{x}^{-2}$
3. $\frac{x^5}{x^2}$
4. $x^{-4}$
5. ${\left(x^3\right)}^4$
6. ${\left(xy\right)}^2$
7. ${\left(\frac{y}{b}\right)}^3$
8. $x^{\frac{2}{3}}$
9. $\frac{x^2{x}^4}{{\left(x^2\right)}^2}$
10. $x^5{x}^{-5}$

Surds

Simplify the following Surds.

1. $\sqrt{9}$
2. $\sqrt{25}$
3. $\sqrt{45}$
4. $\sqrt{63}$
5. $\sqrt{100}$
6. $\sqrt{48}$
7. $\sqrt{98}$
8. $\sqrt{75}$
9. $\sqrt{32}$
10. $\sqrt{320}$
11. $\sqrt{256}$
12. $\sqrt{\frac{9}{36}}$
13. $\sqrt[3]{\frac{27}{125}}$
14. $\sqrt{\frac{162}{200}}$
15. $\sqrt{\frac{75}{3}}$
16. $\sqrt{\frac{112}{72}}$

    Rationalize the Denominator

17. $\frac{2}{\sqrt{4}}$
18. $\frac{8}{4+\sqrt{26}}$
19. $\frac{12}{12-\sqrt{76}}$
20. $\frac{3}{3-\sqrt{65}}$
21. $\frac{9}{9+\sqrt{9}}$