Video Transcript
Given that 𝑎 is equal to six minus
seven times the square root of three and 𝑏 is equal to negative seven minus seven
times the square root of three, find the value of 𝑎 plus 𝑏.
We first substitute the expression
for 𝑎 and 𝑏 to see that 𝑎 plus 𝑏 is equal to six minus seven times the square
root of three plus negative seven minus seven times the square root of three. We can then use the associative and
commutative properties of addition for real numbers to reorder the terms so the
rational numbers are grouped separately from the irrational numbers. We note that six plus negative
seven is equal to six minus seven, which equals negative one.
We recall that for any integers 𝑎,
𝑏, and 𝑐, where 𝑐 is non negative, we have 𝑎 times the square root of 𝑐 plus 𝑏
times the square root of 𝑐 equal to 𝑎 plus 𝑏 times the square root of 𝑐. This means that negative seven
times the square root of three plus negative seven times the square root of three is
equal to negative seven plus negative seven multiplied by the square root of three,
which equals negative 14 times the square root of three.
Therefore, the value of 𝑎 plus 𝑏
simplifies to the expression negative one minus 14 times the square root of
three.
