Advertisements
Advertisements
प्रश्न
Simplify the following expressions:
`(sqrt5 - sqrt3)^2`
Advertisements
उत्तर
We know that `(a - b)^2 = a^2 + b^2 - 2ab`. We will use this property to simplify the expression
`(sqrt5 - sqrt3)`
`∴ (sqrt5 - sqrt3)^2 = (sqrt5)^2 + (sqrt3)^2 - 2 xx sqrt5 xx sqrt3`
`= sqrt5 xx sqrt5 + sqrt3 xx sqrt3 - 2 xx sqrt(5 xx 3)`
`= sqrt(5 xx 5) + sqrt(3 xx 3) - 2 xx sqrt(5 xx 3)`
`= (5^2)^(1/2) + (3^2)^(1/2) - 2sqrt15`
`= 5^1 + 3^1 - 2sqrt15`
`= 8 - 2sqrt15`
Hence the value of expression is `8 - 2sqrt15`
APPEARS IN
संबंधित प्रश्न
Rationalise the denominator of the following:
`1/sqrt7`
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`
`(sqrt2 - 1)/sqrt5`
Rationales the denominator and simplify:
`(5 + 2sqrt3)/(7 + 4sqrt3)`
In the following determine rational numbers a and b:
`(5 + 3sqrt3)/(7 + 4sqrt3) = a + bsqrt3`
If \[a = \sqrt{2} + 1\],then find the value of \[a - \frac{1}{a}\].
Simplify \[\sqrt{3 + 2\sqrt{2}}\].
Simplify the following:
`sqrt(24)/8 + sqrt(54)/9`
Simplify the following:
`root(4)(81) - 8root(3)(216) + 15root(5)(32) + sqrt(225)`
Rationalise the denominator of the following:
`(4sqrt(3) + 5sqrt(2))/(sqrt(48) + sqrt(18))`
Find the value of `4/((216)^(-2/3)) + 1/((256)^(- 3/4)) + 2/((243)^(- 1/5))`
