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
Represent `sqrt9.3` on the number line.
Simplify of the following:
`root(3)4 xx root(3)16`
Rationalise the denominator of the following
`sqrt2/sqrt5`
Express the following with rational denominator:
`(sqrt3 + 1)/(2sqrt2 - sqrt3)`
Write the value of \[\left( 2 + \sqrt{3} \right) \left( 2 - \sqrt{3} \right) .\]
Write the reciprocal of \[5 + \sqrt{2}\].
Classify the following number as rational or irrational:
`1/sqrt2`
Simplify the following expression:
`(3+sqrt3)(3-sqrt3)`
Value of (256)0.16 × (256)0.09 is ______.
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.
`sqrt(2)/(2 + sqrt(2)`
