Advertisements
Advertisements
प्रश्न
Simplify \[\sqrt{3 + 2\sqrt{2}}\].
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+2xx 1xx sqrt2)`
` = sqrt((sqrt2)^2 + (1)^2 + 2 xx 1 xx sqrt2)`
` = sqrt((sqrt2+1))^2`
` = sqrt2 +1`
Hence the value of given expression is ` sqrt2 +1`.
APPEARS IN
संबंधित प्रश्न
Classify the following numbers as rational or irrational:
`2-sqrt5`
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`
`3/sqrt10`
Express the following with rational denominator:
`1/(2sqrt5 - sqrt3)`
Express the following with rational denominator:
`(6 - 4sqrt2)/(6 + 4sqrt2)`
Express the following with rational denominator:
`(3sqrt2 + 1)/(2sqrt5 - 3)`
Value of (256)0.16 × (256)0.09 is ______.
Rationalise the denominator of the following:
`16/(sqrt(41) - 5)`
Rationalise the denominator of the following:
`sqrt(6)/(sqrt(2) + sqrt(3))`
