Advertisements
Advertisements
Question
Prove that:
`sqrt(1/4)+(0.01)^(-1/2)-(27)^(2/3)=3/2`
Advertisements
Solution
We have to prove that `sqrt(1/4)+(0.01)^(-1/2)-(27)^(2/3)=3/2`
Let x = `sqrt(1/4)+(0.01)^(-1/2)-(27)^(2/3)`
`=sqrt(1/2^2)+((0.01xx100)/(1xx100))^(-1/2)-(3^3)^(2/3)`
`=1/2+1/(100)^(-1/2)-3^(3xx2/3)`
`=1/2+1/(1/100^(1/2))-3^2`
`=1/2+1/(1/(10xx10)^(1/2))-3^2`
`=1/2+1/(1/10^(2xx1/2))-3^2`
`=1/2+1/(1/10)-3^2`
`=1/2+1xx10/1-3xx3`
`=1/2+10-9`
`=3/2`
Hence, `sqrt(1/4)+(0.01)^(-1/2)-(27)^(2/3)=3/2`
APPEARS IN
RELATED QUESTIONS
Simplify the following
`3(a^4b^3)^10xx5(a^2b^2)^3`
Solve the following equation for x:
`4^(2x)=1/32`
Show that:
`[{x^(a(a-b))/x^(a(a+b))}div{x^(b(b-a))/x^(b(b+a))}]^(a+b)=1`
If `27^x=9/3^x,` find x.
Find the value of x in the following:
`2^(x-7)xx5^(x-4)=1250`
Solve the following equation:
`3^(x-1)xx5^(2y-3)=225`
If x = 2 and y = 4, then \[\left( \frac{x}{y} \right)^{x - y} + \left( \frac{y}{x} \right)^{y - x} =\]
The simplest rationalising factor of \[\sqrt[3]{500}\] is
If \[x + \sqrt{15} = 4,\] then \[x + \frac{1}{x}\] =
Find:-
`32^(2/5)`
