Duplicate ratio of $a : b$ will be:

\sqrt{a} : \sqrt{b}

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a^{3} : b^{3}

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a^{2} : b^{2}

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\sqrt[3]{a} : \sqrt[3]{b}

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Solution

The correct option is B $a^{2} : b^{2}$
Duplicate ratio of any two numbers mean the ratio of their squares.
Thus if $\frac{a}{b}$ is the ratio the duplicate ratio will be the squares of the numbers.
So the duplicate ratio is $\frac{a^{2}}{b^{2}}$

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Similar questions

a^{2} b^{2} c^{2} (a^{- 3} + b^{- 3} + c^{- 3}) = (a^{3} + b^{3} + c^{3})

Q. If

a + b + c = 1; a^{2} + b^{2} + c^{2} = 2; a^{3} + b^{3} + c^{3} = 3

, then

Q. Which of the following equations are correct?

(i) (a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2 (a b + b c + c a)

(i i) (a + b)^{3} = a^{3} + b^{3} + 3 a b (a - b)

(i i i) (a - b)^{3} = a^{3} - b^{3} - 3 a b (a + b)

(i v) a^{2} - b^{2} = (a + b) (a - b)

Q. Simplify the following expressions.

\frac{a^{2} - b^{2}}{a - b} - \frac{a^{3} - b^{3}}{a^{2} - b^{2}}

Which of the following equation/s is/are correct?

$i) (a + b + c)^{2} = a^{2} + b^{2} + c^{2} - 2 (a b + b c + c a)$
$i i) (a + b)^{3} = a^{3} + b^{3} + 3 a b (a - b)$
$i i i) (a - b)^{3} = a^{3} - b^{3} - 3 a b (a + b)$
$i v) a^{2} - b^{2} = (a + b) (a - b)$

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Duplicate ratio of a:b will be:

The correct option is B a2:b2Duplicate ratio of any two numbers mean the ratio of their squares.Thus if ab is the ratio the duplicate ratio will be the squares of the numbers.So the duplicate ratio is a2b2

Duplicate ratio of $a : b$ will be:

The correct option is B $a^{2} : b^{2}$
Duplicate ratio of any two numbers mean the ratio of their squares.
Thus if $\frac{a}{b}$ is the ratio the duplicate ratio will be the squares of the numbers.
So the duplicate ratio is $\frac{a^{2}}{b^{2}}$