Quantitative Aptitude ยท Mathematics

Algebraic Simplification

151 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 following expression using the Ekadhikena Purvena Sutra: 12345 + 12346 + 12347 + 12348 + 12349 + 12350.

  1. 74125

  2. 75125

  3. 76125

  4. 77125
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The Ekadhikena Purvena Sutra states that the sum of a series of consecutive numbers can be found by multiplying the number of terms by the middle term. In this case, there are 6 terms, and the middle term is 12347. Therefore, the sum of the series is 6 * 12347 = 74125.

Multiple choice

Simplify the following expression using the Vyashtisamutpatti Sutra: (12345 + 6789) - (12345 - 6789).

  1. 13578

  2. 25134

  3. 12514

  4. 24690
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The Vyashtisamutpatti Sutra states that the difference between two numbers can be found by subtracting the smaller number from the larger number. In this case, (12345 + 6789) - (12345 - 6789) = 12345 + 6789 - 12345 + 6789 = 13578.

Multiple choice

Simplify the expression: (x^2 + 2x + 1) - (x^2 - 3x + 2)

  1. 5x - 1

  2. 5x + 1

  3. 5x - 3

  4. 5x + 3
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

To simplify the expression, we can combine like terms. (x^2 + 2x + 1) - (x^2 - 3x + 2) = x^2 + 2x + 1 - x^2 + 3x - 2 = 5x - 1.

Multiple choice

Simplify the expression: (3x^2y^3)^2

  1. 9x^4y^6

  2. 9x^6y^6

  3. 9x^6y^9

  4. 9x^4y^9
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

To simplify the expression, we can use the power of a power rule, which states that (a^m)^n = a^(m * n). Therefore, (3x^2y^3)^2 = 3^(2) * (x^2)^2 * (y^3)^2 = 9x^4y^6.

Multiple choice

Simplify the expression: (x - 2)(x + 3)

  1. x^2 - x - 6

  2. x^2 + x - 6

  3. x^2 - 5x + 6

  4. x^2 + 5x + 6
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

To simplify the expression, we can use the distributive property. (x - 2)(x + 3) = x(x + 3) - 2(x + 3) = x^2 + 3x - 2x - 6 = x^2 + x - 6.

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: $$\sqrt{16} + \sqrt{49} - \sqrt{25}$$ $$4 + 7 - 5$$ $$14$$