Advertisements
Advertisements
Question
Write the value of \[\left( 2 + \sqrt{3} \right) \left( 2 - \sqrt{3} \right) .\]
Advertisements
Solution
Given that
`(2+sqrt3)(2-sqrt3)`
It can be simplified as
`(2+sqrt3)(2-sqrt3) = 2 xx2-2xxsqrt3+2xx sqrt3 - (sqrt3)^2`
` = 4-2sqrt3+2sqrt3 - `
`= 4-3`
` = 1`
APPEARS IN
RELATED QUESTIONS
Simplify the following expressions:
`(sqrt5 - 2)(sqrt3 - sqrt5)`
Simplify the following expressions:
`(3 + sqrt3)(3 - sqrt3)`
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`
`(sqrt5 + 1)/sqrt2`
Rationales the denominator and simplify:
`(1 + sqrt2)/(3 - 2sqrt2)`
Find the values the following correct to three places of decimals, it being given that `sqrt2 = 1.4142`, `sqrt3 = 1.732`, `sqrt5 = 2.2360`, `sqrt6 = 2.4495` and `sqrt10 = 3.162`
`(1 + sqrt2)/(3 - 2sqrt2)`
Classify the following number as rational or irrational:
`(3+sqrt23)-sqrt23`
Rationalise the denominator of the following:
`16/(sqrt(41) - 5)`
Rationalise the denominator of the following:
`sqrt(6)/(sqrt(2) + sqrt(3))`
Find the value of a and b in the following:
`(sqrt(2) + sqrt(3))/(3sqrt(2) - 2sqrt(3)) = 2 - bsqrt(6)`
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.
`4/sqrt(3)`
