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NABTEB Mathematics 2026 Past Questions & Explanations

Try NABTEB Mathematics 2026 questions as a free quiz — select your answers, submit, and see your score with a full explanation for every one.

  1. 1.
    Evaluate 25\sqrt{25}.
    Show explanation
    25=5\sqrt{25} = 5 because 52=255^2 = 25.
  2. 2.
    Simplify 36+49\sqrt{36} + \sqrt{49}.
    Show explanation
    36=6\sqrt{36} = 6 and 49=7\sqrt{49} = 7. Therefore, 6+7=136 + 7 = 13.
  3. 3.
    Find the value of 81−16\sqrt{81} - \sqrt{16}.
    Show explanation
    81=9\sqrt{81} = 9 and 16=4\sqrt{16} = 4. Thus, 9−4=59 - 4 = 5.
  4. 4.
    Express 50\sqrt{50} in its simplest form.
    Show explanation
    50=25×2=252=52\sqrt{50} = \sqrt{25 \times 2} = \sqrt{25}\sqrt{2} = 5\sqrt{2}.
  5. 5.
    Simplify 35+253\sqrt{5} + 2\sqrt{5}.
    Show explanation
    Since the surds are alike, add the coefficients: 3+2=53 + 2 = 5. Therefore, 35+25=553\sqrt{5} + 2\sqrt{5} = 5\sqrt{5}.
  6. 6.
    Simplify 12+27\sqrt{12} + \sqrt{27}.
    Show explanation
    12=23\sqrt{12} = 2\sqrt{3} and 27=33\sqrt{27} = 3\sqrt{3}. Thus, 23+33=532\sqrt{3} + 3\sqrt{3} = 5\sqrt{3}.
  7. 7.
    Rationalize the denominator of 35\frac{3}{\sqrt{5}}.
    Show explanation
    Multiply numerator and denominator by 5\sqrt{5}: 35×55=355\frac{3}{\sqrt{5}} \times \frac{\sqrt{5}}{\sqrt{5}} = \frac{3\sqrt{5}}{5}.
  8. 8.
    Simplify (3+2)(3−2)(\sqrt{3} + \sqrt{2})(\sqrt{3} - \sqrt{2}).
    Show explanation
    Using the difference of two squares: (3)2−(2)2=3−2=1(\sqrt{3})^2 - (\sqrt{2})^2 = 3 - 2 = 1.
  9. 9.
    Evaluate (25)2(2\sqrt{5})^2.
    Show explanation
    (25)2=22×(5)2=4×5=20(2\sqrt{5})^2 = 2^2 \times (\sqrt{5})^2 = 4 \times 5 = 20.
  10. 10.
    Simplify 483\frac{\sqrt{48}}{\sqrt{3}}.
    Show explanation
    483=483=16=4\frac{\sqrt{48}}{\sqrt{3}} = \sqrt{\frac{48}{3}} = \sqrt{16} = 4.
  11. 11.
    Find the value of 64\sqrt{64}.
    Show explanation
    64=8\sqrt{64} = 8 because 82=648^2 = 64.
  12. 12.
    Evaluate 100−36\sqrt{100} - \sqrt{36}.
    Show explanation
    100=10\sqrt{100} = 10 and 36=6\sqrt{36} = 6. Therefore, 10−6=410 - 6 = 4.
  13. 13.
    Simplify 29+162\sqrt{9} + \sqrt{16}.
    Show explanation
    29+16=2(3)+4=6+4=102\sqrt{9} + \sqrt{16} = 2(3) + 4 = 6 + 4 = 10.
  14. 14.
    Express 72\sqrt{72} in its simplest form.
    Show explanation
    72=36×2=62\sqrt{72} = \sqrt{36 \times 2} = 6\sqrt{2}.
  15. 15.
    Simplify 73−237\sqrt{3} - 2\sqrt{3}.
    Show explanation
    Since the surds are alike, subtract the coefficients: 7−2=57 - 2 = 5. Thus, 535\sqrt{3}.
  16. 16.
    Simplify 18+8\sqrt{18} + \sqrt{8}.
    Show explanation
    18=32\sqrt{18} = 3\sqrt{2} and 8=22\sqrt{8} = 2\sqrt{2}. Therefore, 32+22=523\sqrt{2} + 2\sqrt{2} = 5\sqrt{2}.
  17. 17.
    Rationalize the denominator of 52\frac{5}{\sqrt{2}}.
    Show explanation
    Multiply numerator and denominator by 2\sqrt{2}: 52×22=522\frac{5}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{5\sqrt{2}}{2}.
  18. 18.
    Evaluate (7)2+(2)2(\sqrt{7})^2 + (\sqrt{2})^2.
    Show explanation
    (7)2=7(\sqrt{7})^2 = 7 and (2)2=2(\sqrt{2})^2 = 2. Thus, 7+2=97 + 2 = 9.
  19. 19.
    Simplify (5+2)(5−2)(\sqrt{5} + 2)(\sqrt{5} - 2).
    Show explanation
    Using the difference of two squares: (5)2−22=5−4=1(\sqrt{5})^2 - 2^2 = 5 - 4 = 1.
  20. 20.
    Simplify 753\frac{\sqrt{75}}{\sqrt{3}}.
    Show explanation
    753=753=25=5\frac{\sqrt{75}}{\sqrt{3}} = \sqrt{\frac{75}{3}} = \sqrt{25} = 5.
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