Advertisements
Advertisements
प्रश्न
Prove that:
`sqrt(1/4)+(0.01)^(-1/2)-(27)^(2/3)=3/2`
उत्तर
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
संबंधित प्रश्न
Simplify the following
`((4xx10^7)(6xx10^-5))/(8xx10^4)`
Prove that:
`1/(1+x^(b-a)+x^(c-a))+1/(1+x^(a-b)+x^(c-b))+1/(1+x^(b-c)+x^(a-c))=1`
Assuming that x, y, z are positive real numbers, simplify the following:
`(x^-4/y^-10)^(5/4)`
Write the value of \[\sqrt[3]{7} \times \sqrt[3]{49} .\]
For any positive real number x, find the value of \[\left( \frac{x^a}{x^b} \right)^{a + b} \times \left( \frac{x^b}{x^c} \right)^{b + c} \times \left( \frac{x^c}{x^a} \right)^{c + a}\].
The value of \[\left\{ 8^{- 4/3} \div 2^{- 2} \right\}^{1/2}\] is
(256)0.16 × (256)0.09
If \[\frac{3^{5x} \times {81}^2 \times 6561}{3^{2x}} = 3^7\] then x =
If \[\sqrt{2^n} = 1024,\] then \[{3^2}^\left( \frac{n}{4} - 4 \right) =\]
Simplify:
`(3/5)^4 (8/5)^-12 (32/5)^6`
