Advertisements
Advertisements
प्रश्न
Simplify \[\sqrt{3 - 2\sqrt{2}}\].
Advertisements
उत्तर
We are asked to simplify`sqrt(3 - 2sqrt2)` It can be written in the form `(a-b)^2 = a^2 +b^2 - 2ab ` as
`sqrt(3-2sqrt2) = sqrt(2 +1 - 2 xx 1 xx sqrt2)`
` = sqrt((sqrt2)^2 + (1)^2 - 2xx 1xxsqrt2)`
` = sqrt((sqrt2 - 1)^2)`
` = sqrt2 - 1`
Hence the value of the given expression is`sqrt2 - 1`.
APPEARS IN
संबंधित प्रश्न
Simplify the following expressions:
`(sqrt5 - sqrt3)^2`
Express the following with rational denominator:
`16/(sqrt41 - 5)`
Rationales the denominator and simplify:
`(1 + sqrt2)/(3 - 2sqrt2)`
In the following determine rational numbers a and b:
`(4 + 3sqrt5)/(4 - 3sqrt5) = a + bsqrt5`
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`
`(3 - sqrt5)/(3 + 2sqrt5)`
if `x= 3 + sqrt8`, find the value of `x^2 + 1/x^2`
If \[\frac{\sqrt{3 - 1}}{\sqrt{3} + 1}\] =\[a - b\sqrt{3}\] then
Rationalise the denominator of the following:
`1/(sqrt7-2)`
Rationalise the denominator of the following:
`sqrt(6)/(sqrt(2) + sqrt(3))`
Simplify:
`64^(-1/3)[64^(1/3) - 64^(2/3)]`
