√5(√8 + √18) can be written in the form a√10 where a is an integer. Find the value of a.
We have:
√5(√8 + √18)
Now, multiply out the brackets (multiply everything inside the brackets by √5). This gives us
√40 + √90
We now need to simplify the SURDs. We know that we want the answer in the form a√10, so we will try to include √10 in both SURDs (and also to get them into a format where we can add them - both need to have the same SURD).
√40 + √90 = √(4x10) + √(9x10) = √4√10 + √9√10 = 2√10 + 3√10 = 5√10
Hence, a = 5.
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