Advertisements
Advertisements
Question
Simplify the following expressions:
`(sqrt5 - 2)(sqrt3 - sqrt5)`
Advertisements
Solution
We can simplify the expression `(sqrt5 - 2)(sqrt3 - sqrt5)` as
`(sqrt5 - 2)(sqrt3 - sqrt5) = sqrt5 xx sqrt3 - sqrt5 xx sqrt5 - 2 xx sqrt3 + 2 xx sqrt5`
`= sqrt15 - sqrt(5 xx 5) - 2sqrt3 + 2sqrt5`
`=sqrt15 - (5^2)^(1/2) - 2sqrt3 +2sqrt5`
`= sqrt15 - (5^2)^(1/2) - 2sqrt3 + 2sqrt5`
`= sqrt15 - 5^1 - 2sqrt3 + 2sqrt5`
Hence the value of the expression is `sqrt15 - 2sqrt3 + 2sqrt5 - 5`
APPEARS IN
RELATED QUESTIONS
Classify the following numbers as rational or irrational:
`2-sqrt5`
Represent `sqrt9.3` on the number line.
Find the value to three places of decimals of the following. It is given that
`sqrt2 = 1.414`, `sqrt3 = 1.732`, `sqrt5 = 2.236` and `sqrt10 = 3.162`
`(2 + sqrt3)/3`
Express the following with rational denominator:
`1/(3 + sqrt2)`
Classify the following number as rational or irrational:
`1/sqrt2`
Simplify the following:
`sqrt(24)/8 + sqrt(54)/9`
Rationalise the denominator of the following:
`sqrt(40)/sqrt(3)`
Rationalise the denominator of the following:
`(3 + sqrt(2))/(4sqrt(2))`
Find the value of a and b in the following:
`(5 + 2sqrt(3))/(7 + 4sqrt(3)) = a - 6sqrt(3)`
Rationalise the denominator in the following and hence evaluate by taking `sqrt(2) = 1.414, sqrt(3) = 1.732` and `sqrt(5) = 2.236`, upto three places of decimal.
`1/(sqrt(3) + sqrt(2))`
