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11 (a) Work out - OCR - GCSE Maths - Question 11 - 2020 - Paper 1

Question 11

11 (a) Work out. $$rac{1}{16}$$ (b) Simplify. $$ ext{√}6 × ext{√}3$$

Worked Solution & Example Answer:11 (a) Work out - OCR - GCSE Maths - Question 11 - 2020 - Paper 1

Step 1

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Answer

To calculate

$rac{1}{16}$ , we can rewrite it in exponent form:

$16^{- rac{1}{2}}$ .

Since 16 can be expressed as $4^2$ , we can substitute:

$4^{2 imes - rac{1}{2}} = 4^{-1} = rac{1}{4}$ .

Step 2

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Answer

To simplify $√6 × √3$ , we can use the property of square roots that states:

$√a × √b = √{a imes b}$ .

Thus,

$√6 × √3 = √{6 imes 3} = √{18}.$

Further simplifying, we notice that 18 can be factored as:

$√{18} = √{9 imes 2} = √9 × √2 = 3√2.$

Therefore, the simplified answer is $3√2$ .

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