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
Simplify the following expressions:
`(4 + sqrt7)(3 + sqrt2)`
Express of the following with rational denominator:
`1/(sqrt6 - sqrt5)`
Rationales the denominator and simplify:
`(3 - sqrt2)/(3 + sqrt2)`
\[\sqrt{10} \times \sqrt{15}\] is equal to
\[\sqrt[5]{6} \times \sqrt[5]{6}\] is equal to
The number obtained on rationalising the denominator of `1/(sqrt(7) - 2)` is ______.
Simplify the following:
`(sqrt(3) - sqrt(2))^2`
Rationalise the denominator of the following:
`sqrt(6)/(sqrt(2) + sqrt(3))`
Simplify:
`(8^(1/3) xx 16^(1/3))/(32^(-1/3))`
If `a = (3 + sqrt(5))/2`, then find the value of `a^2 + 1/a^2`.
