General Certificate Of Secondary Education (GCSE) Maths Practice Exam

If you have a/√b, which expression is equal to it?

(a√b)/b (a/√b) x (√b/√b) (a x b)/(√b x √b) √(a/b)

Correct Answer:

(a/√b) x (√b/√b)

Explanation:

To understand why the expression \((a/√b) \times (√b/√b)\) is equal to \(a/√b\), let’s break it down. Starting with the expression \(a/√b\), multiplying it by \(√b/√b\) is effectively multiplying by a form of 1, since \(√b/√b\) is equivalent to 1 as long as \(b\) is positive and not equal to zero. This multiplication does not change the value of the original expression, but it transforms it into a different form. Carrying out the multiplication, we have: \[ \frac{a}{\sqrt{b}} \times \frac{\sqrt{b}}{\sqrt{b}} = \frac{a \cdot \sqrt{b}}{\sqrt{b} \cdot \sqrt{b}} = \frac{a \cdot \sqrt{b}}{b} \] Here, we find that the numerator becomes \(a \cdot \sqrt{b}\) and the denominator becomes \(b\) (since \(\sqrt{b} \cdot \sqrt{b} = b\)). The resulting expression

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