√5(√8 + √18) can be written in the form a√10 where a is an integer - Edexcel - GCSE Maths - Question 13 - 2018 - Paper 1
Question 13
√5(√8 + √18) can be written in the form a√10 where a is an integer.
Find the value of a.
a = ________________
Worked Solution & Example Answer:√5(√8 + √18) can be written in the form a√10 where a is an integer - Edexcel - GCSE Maths - Question 13 - 2018 - Paper 1
Step 1
Step 1: Simplify √8 + √18
96%
114 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
First, we need to simplify the expression inside the square root. We know that:
√8=√(4imes2)=√4imes√2=2√2
And for √18:
√18=√(9imes2)=√9imes√2=3√2
Now, substituting these back into the original expression, we get:
√8+√18=2√2+3√2=5√2
Step 2
Step 2: Combine with √5
99%
104 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
Next, we substitute our simplification into the expression:
√5(√8+√18)=√5(5√2)=5√(5imes2)=5√10
Step 3
Step 3: Identify the value of a
96%
101 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
From our manipulation, we see that the expression can be written as:
5√10
This corresponds to the form a√10, where we identify that a = 5.
