Write √5 ( √8 + √18 ) in the form a√10, where a is an integer, without using a calculator.

We start by expanding the brackets : (√5 x √8) + (√5 x √18). A common mistake here is to attempt to add √8 and √18 together. We can't do this because of algebra rules. BIDMAS states that multiplication is done before addition. This does not change simply because the two numbers being added together are in brackets!Multiplying two square roots together means multiplying the numbers int he square roots and they become one square root: √40 + √90.5 x 18 can easily be worked out in your head by doing (5 x 10) + (5 x 8) = 50 + 40 = 90.We know that we are looking for the answer in the form a√10, so we look to split up the square roots to leave √10: (√4 √10) + (√9 √10).This then leaves us with nice square numbers in front of the √10: 2√10 + 3√10.By the addition rule of square roots, we get: 5√10 = √5 ( √8 + √18 ), so a =5.