Advertisements
Advertisements
प्रश्न
Simplify the following expressions:
`(2sqrt5 + 3sqrt2)^2`
Advertisements
उत्तर
We know that `(a + b)^2 = a^2 + b^2 + 2ab`. We will use this property to simplify the expression
`(2sqrt5 + 3sqrt2)^2`
`∴ (2sqrt5 + 3sqrt2)^2 = (2sqrt5)^2 + (3sqrt2)^2 + 2 xx 2sqrt5 xx 3 sqrt2`
`= 2sqrt5 xx 2sqrt5 + 3sqrt2 xx 3sqrt2 + 2 xx 2sqrt5 xx 3sqrt2`
`= 2 xx 2sqrt(5 xx 5) + 3 xx 3sqrt(2 xx 2) + 2 xx 2 xx 3sqrt(5 xx 2)`
`= 4(5^2)^(1/2) + 9(2^2)^(1/2) + 12sqrt10`
`= 4 xx 5^1 + 9 xx 2^1 + 12sqrt10`
` = 20 + 18 + 12sqrt10`
`= 38 + 12sqrt10`
Hence the value of expression is `38 + 12sqrt10`
APPEARS IN
संबंधित प्रश्न
Simplify of the following:
`root(4)1250/root(4)2`
Rationalise the denominator of the following:
`3/(2sqrt5)`
Express the following with rational denominator:
`(sqrt3 + 1)/(2sqrt2 - sqrt3)`
Express each one of the following with rational denominator:
`(b^2)/(sqrt(a^2 + b^2) + a)`
Rationales the denominator and simplify:
`(2sqrt3 - sqrt5)/(2sqrt2 + 3sqrt3)`
Simplify `(7 + 3sqrt5)/(3 + sqrt5) - (7 - 3sqrt5)/(3 - sqrt5)`
\[\sqrt[5]{6} \times \sqrt[5]{6}\] is equal to
The number obtained on rationalising the denominator of `1/(sqrt(7) - 2)` is ______.
Rationalise the denominator of the following:
`(3 + sqrt(2))/(4sqrt(2))`
Simplify:
`[((625)^(-1/2))^((-1)/4)]^2`
