Simplification Questions and Answers – Free Practice!
Refer Concepts for Simplification
Q. 1 Simplify: \( \frac{(45)^2 – (15)^2}{30} \)
Check Solution
Ans: A
Use the identity $ a^2 – b^2 = (a – b)(a + b) $, then divide: $ \frac{30 \times 60}{30} = 60 $
Q. 2 Simplify: \( \sqrt{2025} + \sqrt{1225} – \sqrt{625} \)
Check Solution
Ans: B
All the given expressions are standard squares. You are not supposed to rememebr squares beyond 30, but if you take out 25 from each fo the expression, it becomes obvious:
Roots: $ 5 (\sqrt{81} + \sqrt{49} – \sqrt{25}) = 55 $
Q. 3 Simplify the expression: \( \frac{2}{5} + \frac{3}{10} – \frac{4}{15} \)
Check Solution
Ans: D
LCM = 30 → $ \frac{12+9-8}{30} = \frac{13}{30} $
Q. 4 Simplify: \( \frac{1}{2} \div \left( \frac{3}{4} \times \frac{2}{3} \right) \)
Check Solution
Ans: C
$ \frac{3}{4} \times \frac{2}{3} = \frac{1}{2}, \frac{1}{2} \div \frac{1}{2} = 1 $
Q. 5 Simplify: \( (3.2)^2 – (1.2)^2 \)
Check Solution
Ans: B
$ a^2 – b^2 = (4.4)(2.0) = 8.8 $
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Q. 6 Simplify: \( \frac{(2 + \frac{1}{2})^2}{(1 + \frac{1}{4})} \)
Check Solution
Ans: A
$ (\frac{5}{2})^2 = \frac{25}{4}, \div \frac{5}{4} = 5 $
Q. 7 Simplify: \( \frac{3}{2} + \frac{4}{3} – \frac{5}{6} \)
Check Solution
Ans: A
Convert to common denominator → $ \frac{9 + 8 – 5}{6} = \frac{12}{6} = 2 $
Q. 8 Simplify: \( \left( \frac{5}{6} \right)^2 + \left( \frac{1}{2} \right)^2 \)
Check Solution
Ans: D
$ \frac{25}{36} + \frac{9}{36} = \frac{34}{36} = \frac{17}{18} $
Q. 9 Simplify: \( \sqrt{144} + \sqrt{121} – \sqrt{81} \)
Check Solution
Ans: C
$ \sqrt{144} = 12, \sqrt{121} = 11, \sqrt{81} = 9 → 12 + 11 – 9 = 14 $
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Q. 10 Simplify: \( \frac{1}{(1 – \frac{1}{2})} + \frac{1}{(1 – \frac{1}{3})} \)
Check Solution
Ans: B
$ \frac{1}{\frac{1}{2}} + \frac{1}{\frac{2}{3}} = 2 + \frac{3}{2} = \frac{7}{2} $
Q. 11 Simplify: $\sqrt{[\frac{2.4 × 2.4)}{(1.2 × 3.6)}]^2 + 1}$
Check Solution
Ans: C
Dividing the fractions by 1.2 will give $ \sqrt{(\frac{4}{3})^2 + 1} = \sqrt{(16+9)/9} = 5/3 $
Q. 12 Simplify: $\sqrt{98} + \sqrt{8}$
Check Solution
Ans: C
$\sqrt{98} + \sqrt{8} = 7\sqrt{2} + 2\sqrt{2} = 9\sqrt{2} = \sqrt{162}$
Q. 13 (48% of 850 + 35% of 960) ÷ (0.2 × 8)
Check Solution
Ans: D
48% of 850 = 408, 35% of 960 = 336, Sum = 744; Denominator = 1.6; 744 ÷ 1.6 = 465
Q. 14 √784 + (56 ÷ 7) × 9 – 15² ÷ 5
Check Solution
Ans: C
√784 = 28, (56÷7)×9 = 72, 15²÷5 = 45; 28 + 72 – 45 = 55
Q. 15 $125 × 8^{2/3} ÷ 5^3$
Check Solution
Ans: A
$8^(2/3) = 4; So (125×4) ÷ 125 = 4$
Q. 16 (42² – 28²) ÷ 14
Check Solution
Ans: A
Use a²−b²=(a−b)(a+b); (42−28)(42+28)/14 = 14×70/14 = 70
Q. 17 (18.75% of 640) + (125 ÷ 25) × 3²
Check Solution
Ans: C
18.75% = 3/16; (3/16)×640=120; (125÷25)×3²=45; Total=165
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