Questions and Answers
What is meant by 'simplifying' an expression in this context?
To write the expression as the sum of a rational and an irrational number.
What is the identity used to prove that (x + y)(x – y) = x² – y² for any real numbers x and y?
Distributive law of multiplication over addition of real numbers.
What is the significance of 'rationalising' the denominator in a fraction?
To make the denominator a rational number.
On a number line, where does the number √2 lie?
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What is the formula to simplify the expression (a + b)(a - b)?
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What is the purpose of using identities like (a + b)² = a² + 2ab + b² in algebraic manipulations?
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What is the benefit of using the distributive law of multiplication over addition of real numbers?
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What is the significance of the identity (a + b)(c + d) = ac + ad + bc + bd?
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What is the difference between a rational and an irrational number?
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How can we simplify an expression like (5 + 7)(2 + 5)?
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