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+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
Rationalise the denominator of each of the following
`3/sqrt5`
In the following determine rational numbers a and b:
`(sqrt11 - sqrt7)/(sqrt11 + sqrt7) = a - bsqrt77`
Write the rationalisation factor of \[7 - 3\sqrt{5}\].
Write the rationalisation factor of \[\sqrt{5} - 2\].
The rationalisation factor of \[2 + \sqrt{3}\] is
Classify the following number as rational or irrational:
`(2sqrt7)/(7sqrt7)`
Simplify the following expression:
`(3+sqrt3)(3-sqrt3)`
Simplify the following:
`4sqrt12 xx 7sqrt6`
Simplify the following:
`root(4)(81) - 8root(3)(216) + 15root(5)(32) + sqrt(225)`
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))`
