Question

If square root of 0.05×0.5×a = 0.005×0.5× square root of b , then a/b is equal to​

Answer 1

Answer:

Given expression = √0.5 x .5 x a = .5 x .05 x √ b

⇒ √.025 x a = 0.25 x ⇒ b

⇒ 0.025a = 0.25 x .025 x b

∴ a/b = (.025 x .025) /.025

= .025

Answer 2

Answer:

a/b equal to $\frac{1}{4000}$

Step-by-step explanation:

Given,

square root of 0.05×0.5×a = 0.005×0.5× square root of b

So,

$\sqrt{(0.05 \times 0.5 \times a)} = 0.005 \times 0.5 \times \sqrt{b}$

$\sqrt{( \frac{005}{100} \times \frac{05}{10} \times a) } = 0.005 \times 0.5 \times \sqrt{b}$

$\sqrt{( \frac{5 \times 5 \times a}{1000} )} = 0.005 \times 0.5 \times \sqrt{b}$

$\sqrt{ \frac{5 \times 5 \times a}{10 \times 10 \times 10} } = 0.005 \times 0.5 \times \sqrt{b}$

$\frac{5 \sqrt{a} }{10 \sqrt{10} } = 0.005 \times 0.5 \times \sqrt{b} \\ \frac{5 \sqrt{a} }{10 \sqrt{10} } = \frac{0005}{1000} \times \frac{5}{10} \times \sqrt{b} \\ \frac{5 \sqrt{a} }{10 \sqrt{10} } = \frac{5 \times 5}{1000 \times 10} \times \sqrt{b} \\ \frac{ \sqrt{a} }{ \sqrt{b} } = \frac{5 \times 5}{1000 \times 10} \times \frac{10 \sqrt{10} }{5} \\ \frac{ \sqrt{a} }{ \sqrt{b} } = \frac{5 \sqrt{10} }{1000}$

We are squaring both side,

$\frac{a}{b} = \frac{25 \times 10}{1000000} \\ \frac{a}{b} = \frac{1}{4000}$

This is a problem of Algebra.

Some important Algebra formulas.

(a + b)² = a² + 2ab + b²

(a − b)² = a² − 2ab − b²

(a + b)³ = a³ + 3a²b + 3ab² + b³

(a - b)³ = a³ - 3a²b + 3ab² - b³

a³ + b³ = (a + b)³ − 3ab(a + b)

a³ - b³ = (a -b)³ + 3ab(a - b)

a² − b² = (a + b)(a − b)

a² + b² = (a + b)² − 2ab

a² + b² = (a − b)² + 2ab

a³ − b³ = (a − b)(a² + ab + b²)

a³ + b³ = (a + b)(a² − ab + b²)

Know more about Algebra,

1) https://brainly.in/question/13024124

2) https://brainly.in/question/1169549