Quantitative Aptitude ยท Mathematics

Algebraic Simplification

146 Questions

Algebraic simplification involves reducing mathematical expressions to their simplest forms using exponent rules and identities. Test takers must manipulate equations to find rapid solutions. This skill is frequently assessed in SSC, banking, and railway quantitative aptitude sections.

Exponent rulesSurd operationsAlgebraic identitiesTrigonometric simplificationLogical expressions

Algebraic Simplification Questions

Multiple choice

Simplify the expression: ( 3^2 \cdot 3^4 )

  1. \( 3^6 \)
  2. \( 3^8 \)
  3. \( 9^6 \)
  4. \( 9^8 \)
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Using the rule of exponents, ( a^m \cdot a^n = a^(m+n) ), we have ( 3^2 \cdot 3^4 = 3^(2+4) = 3^8 ).

Multiple choice

Simplify the expression: ( (25^2)^3 )

  1. \( 5^6 \)
  2. \( 5^9 \)
  3. \( 5^{12} \)
  4. \( 5^{15} \)
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Using the rule of exponents, ( (a^m)^n = a^(m \cdot n) ), we have ( (25^2)^3 = 25^(2 \cdot 3) = 25^6 = 5^{2 \cdot 6} = 5^{12} ).

Multiple choice

Simplify the expression: ( \sqrt{49} - \sqrt{16} )

  1. \( 1 \)
  2. \( 3 \)
  3. \( 5 \)
  4. \( 7 \)
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Simplifying the expression, we have ( \sqrt{49} - \sqrt{16} = 7 - 4 = 3 ).

Multiple choice

Simplify the expression: ( (\sqrt{9})^2 )

  1. \( 3 \)
  2. \( 6 \)
  3. \( 9 \)
  4. \( 18 \)
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Simplifying the expression, we have ( (\sqrt{9})^2 = 9^2 = 81 ). Therefore, the answer is ( 9 ).

Multiple choice

Simplify the expression: ( \sqrt{100} + \sqrt{25} )

  1. \( 15 \)
  2. \( 20 \)
  3. \( 25 \)
  4. \( 30 \)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Simplifying the expression, we have ( \sqrt{100} + \sqrt{25} = 10 + 5 = 15 ).

Multiple choice

Simplify the expression: ( \sqrt[3]{27} \cdot \sqrt[3]{9} )

  1. \( 3 \)
  2. \( 6 \)
  3. \( 9 \)
  4. \( 18 \)
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Using the rule of exponents, ( a^{m/n} \cdot a^{p/n} = a^{(m+p)/n} ), we have ( \sqrt[3]{27} \cdot \sqrt[3]{9} = \sqrt[3]{27 \cdot 9} = \sqrt[3]{243} = 3 \cdot 3 \cdot 3 = 9 ).

Multiple choice

Simplify the expression: ( (3^2)^3 \cdot 3^4 )

  1. \( 3^9 \)
  2. \( 3^{10} \)
  3. \( 3^{12} \)
  4. \( 3^{15} \)
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Using the rule of exponents, ( (a^m)^n = a^(m \cdot n) ), we have ( (3^2)^3 \cdot 3^4 = 3^(2 \cdot 3) \cdot 3^4 = 3^6 \cdot 3^4 = 3^(6+4) = 3^{10} ).

Multiple choice

Simplify the expression: ( \sqrt[6]{64} \cdot \sqrt[6]{16} )

  1. \( 2 \)
  2. \( 4 \)
  3. \( 8 \)
  4. \( 16 \)
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Using the rule of exponents, ( a^{m/n} \cdot a^{p/n} = a^{(m+p)/n} ), we have ( \sqrt[6]{64} \cdot \sqrt[6]{16} = \sqrt[6]{64 \cdot 16} = \sqrt[6]{1024} = 2 \cdot 2 \cdot 2 \cdot 2 = 4 ).

Multiple choice

Simplify the following expression: $$(3x + 2y) - (2x - 3y)$$

  1. x + 5y

  2. x - y

  3. 5x + y

  4. x + y
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

To simplify the expression, we can distribute the negative sign to the terms inside the second parentheses: $$(3x + 2y) - (2x - 3y)$$ $$3x + 2y - 2x + 3y$$ Combining like terms, we get: $$x + 5y$$

Multiple choice

Simplify the following expression: $$\sqrt{16} + \sqrt{49} - \sqrt{25}$$

  1. 12

  2. 14

  3. 16

  4. 18
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Simplifying the expression, we get: $$\sqrt{16} + \sqrt{49} - \sqrt{25}$$ $$4 + 7 - 5$$ $$14$$

Multiple choice

Simplify the following expression: $$\frac{x^2 + 2x + 1}{x + 1}$$

  1. x + 2

  2. x + 1

  3. x - 1

  4. x - 2
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

To simplify the expression, we can use polynomial long division: $$rac{x^2 + 2x + 1}{x + 1} = x + 1$$ The remainder is 0, which means that the expression simplifies to $$x + 1$$. Therefore, the answer is $$x + 1$$.