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If \( \sqrt{5}(\sqrt{8} + \sqrt{18}) \) can be written in the form \( a \sqrt{10} \) where \( a \) is an integer - Edexcel - GCSE Maths - Question 13 - 2018 - Paper 1

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Question 13

If-\(-\sqrt{5}(\sqrt{8}-+-\sqrt{18})-\)-can-be-written-in-the-form-\(-a-\sqrt{10}-\)-where-\(-a-\)-is-an-integer-Edexcel-GCSE Maths-Question 13-2018-Paper 1.png

If \( \sqrt{5}(\sqrt{8} + \sqrt{18}) \) can be written in the form \( a \sqrt{10} \) where \( a \) is an integer. Find the value of \( a \).

Worked Solution & Example Answer:If \( \sqrt{5}(\sqrt{8} + \sqrt{18}) \) can be written in the form \( a \sqrt{10} \) where \( a \) is an integer - Edexcel - GCSE Maths - Question 13 - 2018 - Paper 1

Step 1

Step 1: Simplify \( \sqrt{8} + \sqrt{18} \)

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Answer

Start by simplifying each square root:

( \sqrt{8} = \sqrt{4 \times 2} = 2\sqrt{2} )

( \sqrt{18} = \sqrt{9 \times 2} = 3\sqrt{2} )

Now, add these together:

( \sqrt{8} + \sqrt{18} = 2\sqrt{2} + 3\sqrt{2} = 5\sqrt{2} )

Step 2

Step 2: Combine with \( \sqrt{5} \)

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Answer

Next, compute ( \sqrt{5}(5\sqrt{2}) ):

( \sqrt{5} \times 5\sqrt{2} = 5\sqrt{10} ) (since ( \sqrt{5} \times \sqrt{2} = \sqrt{10} ))

Step 3

Step 3: Identify \( a \)

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Answer

Thus, ( 5\sqrt{10} ) can be expressed as ( a\sqrt{10} ) where ( a = 5 ). Therefore, the value of ( a ) is:

( a = 5 )

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