Tag: powers and roots

$(23)^2$
$a=2, b=3$

$\therefore (23)^2=529$

$(52)^2$
$a=5, b=2$

$\therefore (52)^2=2704$

$12 \times 12 =144, 12^2 = 144$. 

$144$ is a square of number $12$.

Therefore, option A is the correct answer.

Let the number be $x.$
As per the problem $\sqrt {x}=2\times \sqrt [ 3 ]{x  } $
Raising both sides by $6$ times
$=(x^{1/2})^6 = 2^6(x^{1/3})^6$
$= x^{1/2\times 6} = 2^6 x^{1/3\times 6}$
or $ x^3 = 64 x^2$
or $x=64$

The square of the number $78$ is $6084$

$Using\quad approximate\quad values,\quad we\quad will\quad calculate\quad the\quad values\quad the\quad given\quad problem\ \quad \quad =\quad { \left( 23.1 \right)  }^{ 2 }+{ \left( 48.6 \right)  }^{ 2 }-{ \left( 39.8 \right)  }^{ 2 }\ \quad \quad =\quad 533.61+2362.96-1584.04\ \quad \quad =\quad 1311.53\ \quad \quad =\quad approx...\quad { \left( 36.21 \right)  }^{ 2 }$

we know 

Take two numbers $3$ and $4$.

Square of a number means multiplying a number with the same number.

Square of $17\times 17 =289$.

Therefore, option B is the correct answer.

Square of  a number means multiply a number with the same number.

$22 \times 22= 22^2  = 484$

Thus the square of number $22$ is $484$.

Therefore, option C is the correct answer.