Advertisements
Advertisements
प्रश्न
Simplify the following expressions:
`(3 + sqrt3)(3 - sqrt3)`
Advertisements
उत्तर
We know that `(a - b)(a + b) = a^2 - b^2`. We will use this property to simplify the expression
`(3 + sqrt3)(3 - sqrt3)`
`∴ (3 + sqrt3)(3 - sqrt3) = (3)^2 - (sqrt3)^2`
`= 3^2 - sqrt3 xx sqrt3`
`= 3 xx 3 - sqrt(3 xx 3)`
`= 9 - (3^2)^(1/2)`
`= 9 - 3^1`
= 6
Hence the value of expression is 6.
APPEARS IN
संबंधित प्रश्न
Simplify the following expressions:
`(3 + sqrt3)(5 - sqrt2)`
Simplify the following expressions:
`(2sqrt5 + 3sqrt2)^2`
Express the following with rational denominator:
`16/(sqrt41 - 5)`
Rationales the denominator and simplify:
`(4sqrt3 + 5sqrt2)/(sqrt48 + sqrt18)`
In the following determine rational numbers a and b:
`(3 + sqrt2)/(3 - sqrt2) = a + bsqrt2`
If \[x = 3 + 2\sqrt{2}\],then find the value of \[\sqrt{x} - \frac{1}{\sqrt{x}}\].
Simplify the following:
`4sqrt(28) ÷ 3sqrt(7) ÷ root(3)(7)`
Find the value of a and b in the following:
`(3 - sqrt(5))/(3 + 2sqrt(5)) = asqrt(5) - 19/11`
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))`
Simplify:
`(7sqrt(3))/(sqrt(10) + sqrt(3)) - (2sqrt(5))/(sqrt(6) + sqrt(5)) - (3sqrt(2))/(sqrt(15) + 3sqrt(2))`
