Tag: square root of non perfect squares

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Multiple choice maths squares and square roots approximation of square roots estimating square roots square root of non perfect squares

Estimate: $\sqrt { 60 } $

  1. $7.7$
  2. $7$
  3. $7.2$
  4. $7.5$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$60$ is in between two perfect squares: $49$, which is ${7}^{2}$ and $64$ which is ${8}^{2}$. The difference between $64$ and $49$ is $15$ so $60$ is little more than $\cfrac{2}{3}$ of the way toward $64$ from $49$. A reasonable estimate for $\sqrt {60}$, then would be about $7.7$ which is a little more than $\cfrac{2}{3}$ toward $8$ from $7$.

Multiple choice maths squares and square roots approximation of square roots estimating square roots square root of non perfect squares

Which of the following is not a perfect square?

  1. $16384$
  2. $23857$
  3. $18496$
  4. $11025$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$16384= 128\times 128$         (perfect square)

$18496=136\times 136$           (perfect square)
$11025=105\times 105$         (perfect square)
$23857 = 1\times  23857$        (prime no. so not a perfect square)
Hence, option B is correct.

Multiple choice maths squares and square roots approximation of square roots estimating square roots square root of non perfect squares

If $x=\sqrt {12}-\sqrt {9},y=\sqrt {13}-\sqrt {10}$ and $z=\sqrt {11}-\sqrt {8}$, then which of the following is true?

  1. $z > x > y$
  2. $z > y > x$
  3. $y > x > z$
  4. $y > z> x$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$x=\sqrt{12}-\sqrt{9}$

$x=2\sqrt{3}-3$
$x=2(1.73)-3$
$x=3.46-3$
$\therefore$   $x=0.46$                    ----- ( 1 )
Now,
$y=\sqrt{13}-\sqrt{10}$
$y=3.60-3.16$
$\therefore$  $y=0.44$                ---- ( 2 )
Now,
$z=\sqrt{11}-\sqrt{8}$
$z=3.32-2.83$
$\therefore$  $z=0.49$             ---- ( 3 )
From ( 1 ), ( 2 ) and ( 3 )
$\Rightarrow$  $0.49>0.46>0.44$
$\therefore$  $z>x>y$

Multiple choice maths squares and square roots approximation of square roots estimating square roots square root of non perfect squares

Find the atleast number which must  be added to each of the following numbers to get a perfect square. Also find the square root of the perfect square numbers.


$a)525$

  1. 4

  2. 3

  3. 1

  4. 6

  5. 12
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
$i)\ 23^2=529$
$\therefore \ $ it will add $4$ to $525$ we get $529$
which is payout square
$\therefore \ 525+4=529=23^2$

$\therefore 4$ should be added


Multiple choice maths squares and square roots approximation of square roots estimating square roots square root of non perfect squares

The value of $\sqrt { \sqrt [ a ]{ { 4 }^{ { a }^{ { a }^{ 2 } } }\sqrt { { 6 }^{ { a }^{ 3 } }\sqrt [ { a }^{ 3 } ]{ { 12 }^{ { a }^{ 6 } }\sqrt [ { a }^{ 4 } ]{ { 18 }^{ { a }^{ 10 } } }  }  }  }  } $ is equal to

  1. $\sqrt {216}$
  2. $\sqrt {72}$
  3. $72$
  4. $216$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$\begin{array}{l} =\sqrt { \sqrt [ a ]{ { { 4^{ { a^{ { a^{ 2 } } } } } }\sqrt { { 6^{ { a^{ 3 } } } }\sqrt [ { { a^{ 3 } } } ]{ { { { 12 }^{ { a^{ 6 } } } }\sqrt [ { { a^{ 4 } } } ]{ { { { 18 }^{ { a^{ 10 } } } } } }  } }  }  } }  }  \ =\sqrt { 4\times 6\times 18\times 12 }  \ =72 \ Hence, \ option\, \, C\, \, is\, correct\, \, answer. \end{array}$