Test: Surds & Indices - Introduction and Examples (with Solutions) - SSS 3 MCQ

A Surd is defined as the root of a quantity that cannot be expressed as a rational number. Examples include √3 and 2√5.
Surds are important in mathematics because they represent irrational numbers that cannot be simplified further.

The number 2 is the base, and 5 is the index in the expression 2⁵, which means 2 is multiplied by itself 5 times.

To solve √(X/0.0081) = ∛0.009, we find that X = 0.000729 after simplifying the equation.
This means X is a very small number that relates to the cube root of 0.009.

The expression simplifies to √36, which equals 6. This involves several steps of simplification through nested square roots.

The calculation simplifies to 54.2 after proper arithmetic operations. This shows the importance of handling decimal multiplication and division accurately.

The expression simplifies to (625)^0.25, which equals 5, demonstrating the laws of indices where exponents are added when multiplying like bases.

The law states that when multiplying powers with the same base, you add the exponents: a^m × aⁿ = a^m+n.

A Surd of order n is a root of a rational number that cannot be simplified to a rational number itself, confirming its irrational status.

√4 is not a Surd because it simplifies to a whole number (2). In contrast, √2, √3, and √5 do not simplify further and are thus considered Surds.

The index in the expression 3⁴ is 4, indicating that 3 is multiplied by itself four times.

9 is a perfect square because it can be expressed as 3 × 3. Perfect squares are numbers whose square roots are whole numbers.

The simplified form of √(x²) is x, assuming x is non-negative. This illustrates the property of square roots that they return the principal (non-negative) root.

The correct expression is (a^m)(aⁿ) = a^m+n, which shows that powers with the same base can be added.

A Surd indicates that the expression cannot be simplified to a rational number, highlighting the presence of irrational values in mathematics.

A Surd like √a is considered a rational number if a is a perfect square since it can be expressed as a whole number. For example, √4 = 2.

The law states that the square root of a product equals the product of the square roots: √(a × b) = √a × √b, which is a fundamental property of roots.

Taking the square root of a negative number results in a complex number, which involves the imaginary unit i, where i = √(-1). This is a key concept in advanced mathematics.