Question

If √_(0.512)/x =3√1000000, then find the value of x

Answer 1

Answer:

= 4/5

Step-by-step explanation:

0.512/x = 512/1000x

cube root of 0.512/x = [(8/10)^3]^1/3 × (1/x)^1/3

8/10 × (1/x)^1/3 = [(100)^3]^1/3

8/10 × (1/x)^1/3 = 100

(8/x)^1/3 = 1000

(8/x)^1/3 = 10^3

8/x = 10

x = 8/10 = 4/5

Answer 2

Step-by-step explanation:

$\mathsf{Given : \dfrac{\sqrt[3]{0.512}}{x} = \sqrt[3]{1000000}}$

$\mathsf{\implies x = \dfrac{\sqrt[3]{0.512}}{\sqrt[3]{1000000}}}$

$\textsf{We know that :}$

$\mathsf{\bigstar\;\;0.512 = 0.8 \times 0.8 \times 0.8 = (0.8)^3}$

$\mathsf{\bigstar\;\;1000000 = 100 \times 100 \times 100 = (100)^3}$

$\mathsf{\implies x = \dfrac{\sqrt[3]{(0.8)^3}}{\sqrt[3]{(100)^3}}}$

$\bigstar\;\;\textsf{We know that : \boxed{\mathsf{\sqrt[n]{a} = a^{\frac{1}{n}}}}}$

$\mathsf{\implies x = \dfrac{[(0.8)^3]^{\frac{1}{3}}}{[(100)^3]^{\frac{1}{3}}}}$

$\mathsf{\implies x = \dfrac{[0.8]^{\frac{3}{3}}}{[100]^{\frac{3}{3}}}}$

$\mathsf{\implies x = \dfrac{0.8}{100}}$

$\mathsf{\implies x = 0.008}$