Multiple Choice

1. Simplify the expression: $(\sqrt{12} + \sqrt{75})(\sqrt{48} - \sqrt{27})$.

   $105$

   $7\sqrt{3}$

   $21\sqrt{3}$

   $21$

2. Expand and simplify: $(3\sqrt{18} - 2\sqrt{8})(5\sqrt{50} + 4\sqrt{32})$.

   $820$

   $410\sqrt{2}$

   $410$

   $205\sqrt{2}$

3. Simplify the expression: $(\sqrt{7} + \sqrt{3} - \sqrt{5})(\sqrt{7} + \sqrt{3} + \sqrt{5})$.

   $5 + 2\sqrt{21}$

   $5 - 2\sqrt{21}$

   $10 - 5\sqrt{5}$

   $15 + 2\sqrt{21}$

4. Expand and simplify: $(2\sqrt{3} - 5)(\sqrt{12} + \sqrt{27})$.

   $30 + 25\sqrt{3}$

   $30 - 5\sqrt{3}$

   $10\sqrt{3} - 25\sqrt{3}$

   $30 - 25\sqrt{3}$

5. Expand and simplify: $(3\sqrt{6} - 2\sqrt{3})^2$.

   $66 + 36\sqrt{2}$

   $66 - 36\sqrt{2}$

   $42 - 36\sqrt{2}$

   $54 - 12\sqrt{18} + 12$

6. Simplify the expression: $(\sqrt{108} - \sqrt{48}) \times (\sqrt{75} + \sqrt{12}) \times \sqrt{3}$.

   $42\sqrt{3}$

   $42$

   $14\sqrt{3}$

   $28\sqrt{3}$

7. Evaluate: $(\sqrt{17} - \sqrt{5})(\sqrt{17} + \sqrt{5}) - (\sqrt{11} - \sqrt{2})(\sqrt{11} + \sqrt{2})$.

   $2\sqrt{3}$

   $3$

   $21$

   $3\sqrt{3}$

8. Expand and simplify: $(4\sqrt{2} + 3\sqrt{5})(2\sqrt{2} - \sqrt{5})$.

   $31 + 2\sqrt{10}$

   $1 + 10\sqrt{2}$

   $1 + 2\sqrt{10}$

   $1 - 2\sqrt{10}$

9. Simplify: $(\sqrt{13} - (2\sqrt{3}))(\sqrt{13} + 2\sqrt{3})$.

   $1 - 4\sqrt{3}$

   $13 - 4\sqrt{3}$

   $25$

   $1$

10. Expand and simplify: $3\sqrt{2}(2\sqrt{6} - \sqrt{24} + 5\sqrt{8})$.

    $6\sqrt{12} - 3\sqrt{48} + 30\sqrt{16}$

    $30\sqrt{2}$

    $12\sqrt{3} + 60$

    $60$

11. Evaluate: $(2 + \sqrt{3})^2 - (2 - \sqrt{3})^2$.

    $4\sqrt{3}$

    $8\sqrt{3}$

    $14$

    $0$

12. Expand and simplify: $(\sqrt{20} + \sqrt{45})(\sqrt{80} - \sqrt{5})$.

    $25\sqrt{5}$

    $75\sqrt{5}$

    $15\sqrt{5}$

    $75$

13. Simplify: $(3\sqrt{2} - 1)(\sqrt{3} + 2)(\sqrt{3} - 2)$.

    $3\sqrt{2} - 1$

    $3\sqrt{2} + 1$

    $-3\sqrt{2} - 1$

    $1 - 3\sqrt{2}$

14. Expand and simplify: $(2\sqrt{5} + \sqrt{10})^2$.

    $20 + 20\sqrt{2} + 10\sqrt{2}$

    $30 + 20\sqrt{2}$

    $30 + 20\sqrt{50}$

    $30 + 10\sqrt{2}$

15. Simplify: $((\sqrt{18} + \sqrt{2}) - \sqrt{50})((\sqrt{18} + \sqrt{2}) + \sqrt{50})$.

    $32 - 50\sqrt{2}$

    $18$

    $-18\sqrt{2}$

    $-18$

16. Expand and simplify: $(3\sqrt{2} - \sqrt{6})(\sqrt{18} + \sqrt{24})$.

    $6 + 6\sqrt{3}$

    $6 - 6\sqrt{3}$

    $18 - 12\sqrt{3} - 12$

    $30 + 6\sqrt{3}$

17. Expand and simplify: $(5\sqrt{3} - 2\sqrt{7})(4\sqrt{3} + 3\sqrt{7})$.

    $102 + 7\sqrt{21}$

    $18 + 7\sqrt{21}$

    $18 - 7\sqrt{21}$

    $18 + 23\sqrt{21}$

18. Simplify: $(\sqrt{72} + \sqrt{2})(\sqrt{200} - \sqrt{50}) + (\sqrt{3} + \sqrt{2})^2$.

    $70 + 5\sqrt{6}$

    $75 - 2\sqrt{6}$

    $75 + 2\sqrt{6}$

    $70 + 2\sqrt{6}$

19. Simplify: $(\sqrt{x} + \sqrt{y})(\sqrt{x} - \sqrt{y})(x + y)$. (Assume $x, y > 0$)

    $x - y$

    $(x-y)(x+y)$

    $x^2 - y^2$

    $x^2 + y^2$

20. Simplify: $( \sqrt{150} - \sqrt{24} )^2 - ( \sqrt{96} + \sqrt{54} )^2$.

    $-240$

    $-144$

    $-192\sqrt{6}$

    $240$

21. A square garden has a side length of $\sqrt{18}$ m. What is its area?

    $18$ m$^2$

    $9$ m$^2$

    $36$ m$^2$

    $3\sqrt{2}$ m$^2$

22. The diagonal of a rectangle is $\sqrt{20}$ m and its breadth is $\sqrt{5}$ m. Find its length.

    $4$ m

    $\sqrt{15}$ m

    $\sqrt{100}$ m

    $2$ m

23. A triangular park has a base of $\sqrt{12}$ m and a height of $\sqrt{3}$ m. What is its area?

    $3$ m$^2$

    $18$ m$^2$

    $\sqrt{15}$ m$^2$

    $6$ m$^2$

24. A rectangular hall has a length of $\sqrt{50}$ m and a breadth of $\sqrt{2}$ m. What is its area?

    $10\sqrt{2}$ m$^2$

    $\sqrt{52}$ m$^2$

    $10$ m$^2$

    $5\sqrt{2}$ m$^2$

25. A circle has a radius of $\sqrt{8}$ m. What is its area in terms of $\pi$?

    $\sqrt{8}\pi$ m$^2$

    $8\pi$ m$^2$

    $2\pi\sqrt{8}$ m$^2$

    $16\pi$ m$^2$

26. A field has sides measuring $\sqrt{18}$ m and $\sqrt{8}$ m. What is the area of the field?

    $12$ m$^2$

    $\sqrt{26}$ m$^2$

    $144$ m$^2$

    $6\sqrt{2}$ m$^2$

27. A rhombus has diagonals measuring $\sqrt{12}$ m and $\sqrt{48}$ m. What is its area?

    $\sqrt{60}$ m$^2$

    $6$ m$^2$

    $12$ m$^2$

    $24$ m$^2$

28. A square tile has a side length of $\sqrt{32}$ cm. What is its area?

    $16$ cm$^2$

    $32$ cm$^2$

    $64$ cm$^2$

    $\sqrt{32}$ cm$^2$

29. A rectangle has a length of $3\sqrt{2}$ m and a breadth of $4\sqrt{3}$ m. What is its area?

    $12\sqrt{6}$ m$^2$

    $7\sqrt{5}$ m$^2$

    $12\sqrt{5}$ m$^2$

    $7\sqrt{6}$ m$^2$

30. A right triangle has legs measuring $\sqrt{27}$ m and $\sqrt{12}$ m. What is its area?

    $\sqrt{39}$ m$^2$

    $6$ m$^2$

    $9$ m$^2$

    $18$ m$^2$

31. A farmer wants to fence a square plot of land with a side length of $\sqrt{45}$ m. What is its area?

    $90$ m$^2$

    $45$ m$^2$

    $2025$ m$^2$

    $\sqrt{45}$ m$^2$

32. A carpet has dimensions of $\sqrt{72}$ m by $\sqrt{2}$ m. What is its area?

    $6\sqrt{2}$ m$^2$

    $\sqrt{74}$ m$^2$

    $12$ m$^2$

    $144$ m$^2$

33. A rectangular piece of land has a length of $5\sqrt{3}$ m and a breadth of $2\sqrt{6}$ m. What is its area?

    $10\sqrt{3}$ m$^2$

    $30\sqrt{2}$ m$^2$

    $7\sqrt{9}$ m$^2$

    $10\sqrt{9}$ m$^2$

34. A wall has a height of $\sqrt{98}$ m and a breadth of $\sqrt{2}$ m. What is its area?

    $\sqrt{100}$ m$^2$

    $14$ m$^2$

    $196$ m$^2$

    $7\sqrt{2}$ m$^2$

35. The diagonal of a square is $\sqrt{128}$ m. What is its area?

    $32$ m$^2$

    $64$ m$^2$

    $\sqrt{128}$ m$^2$

    $128$ m$^2$