Tag: powers and roots

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Questions Related to powers and roots

Multiple choice maths square and square root perfect square or square number squares and triangles powers and roots

Find the value of each of the following, using the column method.
$(23)^2$
$(52)^2$

  1. 549, 2724

  2. 549, 2704

  3. 529, 2724

  4. 529, 2704
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

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

$i$ $ii$ $iii$
$a^2$ $2ab$ $b^2$
$4$$1$           $\underline { 5 }$ $12$$+0$           $1\underline { 2 }$ $\underline { 9 }$

$\therefore (23)^2=529$

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

$i$ $ii$ $iii$
$a^2$ $2ab$ $b^2$
$25$$+2$          $\underline { 27 }$ $20$$+0$          $2\underline { 0 }$ $\underline { 4 }$

$\therefore (52)^2=2704$

Multiple choice maths square and square root perfect square or square number squares and triangles powers and roots

Find the number whose square root is twice of its cubic root.

  1. $128$
  2. $64$
  3. $16$
  4. $4$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

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 $x=64$

Multiple choice maths square and square root perfect square or square number squares and triangles powers and roots

Solve:$(23.1)^2+(48.6)^2-(39.8)^2$

  1. $(36.21)^2$
  2. $\sqrt{12.8}$
  3. $163.84$
  4. $12.8$

  5. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

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

Multiple choice maths square and square root perfect square or square number squares and triangles powers and roots

Write the $(T)$ of false $(F)$ for the following statements.
The product of two square number is a square number.

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Take two numbers $3$ and $4$.

$\Rightarrow$  $3^2=9$ and $4^2=16$
$\Rightarrow$  Product of squares of $3$ and $4$ $=9\times 16=144$
We know, that $144$ is a square if $12$.
$\therefore$  The given statement " The product of two squares number is a square number " is true.