Tag: squares and square roots

Questions Related to squares and square roots

Determine
(a) $\sqrt{147} \times \sqrt{243} \$

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

  1. $189$

  2. $209$

  3. $197$

  4. $138$

Show answer
Correct Option: A
Explanation:

$√143 = √3  × √49 = √3  × 7$
$√243 = √3  × √81 = √3  × 9$
$√143  ×√243  = 3  × 9  × 7 = 189$

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

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

  1. $z > x > y$

  2. $z > y > x$

  3. $y > x > z$

  4. $y > z> x$

Show answer
Correct Option: A
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 )
$\Rightarrow$  $0.49>0.46>0.44$
$\therefore$  $z>x>y$

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.


$a)525$

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

  1. 4

  2. 3

  3. 1

  4. 6

  5. 12

Show answer
Correct Option: A
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


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

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

  1. $\sqrt {216}$

  2. $\sqrt {72}$

  3. $72$

  4. $216$

Show answer
Correct Option: C
Explanation:

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

The approximate value of $\sqrt{(1.97)^2+(4.02)^2+(3.98)^2}$.

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

  1. $5.99$

  2. $5.099$

  3. $5.009$

  4. $5.734$

Show answer
Correct Option: A
Explanation:

According to Question

$\sqrt{(2-0.03)^2+(4+0.02)^2+(4-0.02)^2}$
Opening Brackets
$\sqrt{(4+0.0009-0.12)+(16+0.0004+0.16)+(16+0.0004-0.16)}$
$\sqrt{36-0.1183}$
$\sqrt{35.8817} \approx 5.99$

The square root of 496 correct to three places of decimal is 22.271
State true or false.

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

  1. True

  2. False

Show answer
Correct Option: A
Explanation:

$\quad \ \quad \quad \quad \quad \quad 22.271\ \quad \quad \quad \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ \quad \quad 2)496.00\quad 00\quad 00\ \quad \quad \quad -4\quad \downarrow \ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ 42)\quad 00\quad 96\ \quad \quad -0084\quad \quad \downarrow \ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ 442)\quad 12\quad 00\ \quad \quad -\quad \quad 0884\quad \quad \downarrow \ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \quad \ 4447)\quad \quad \quad \quad \quad \quad 316\quad 00\quad \ \quad \quad \quad \quad \quad \quad \quad \quad \quad -31129\quad \quad \downarrow \ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ 44541)\qquad \qquad \qquad \quad \quad \quad \quad 471\quad 00\ \qquad \qquad \qquad \qquad \qquad -\quad \quad 44541\ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad 2559\ Rounding\quad off\quad :\quad 22.271\ \ $

Find the square root of $\displaystyle 3 \frac{4}{5}$  to two decimal places 

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

  1. $1.95$

  2. $1.96$

  3. $1.84$

  4. $1.94$

Show answer
Correct Option: A
Explanation:

  $\displaystyle 3 \dfrac{4}{5}$
$=\dfrac{19}{5}$
$=3.8$

$1$$1$ $3.8$$1$
$29$$9$ $280$$261$
$384$$4$ $1900$$1536$
$3889$ $36400$$35001$                     

Therefore,
Square root of $\displaystyle 3 \frac{4}{5}=1.949$
                              $=1.95$

State true or false:

The square root of 0.008 correct to three decimal places is 0.089.

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

  1. True

  2. False

Show answer
Correct Option: A
Explanation:

$\quad \ \quad \quad \quad \quad \quad 0.089\ \quad \quad \quad \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ \quad \quad 0)\quad 0.00\quad 80\quad 00\ \quad \quad \quad -0.00\quad \downarrow \ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ 8)\quad \quad 00\quad 80\ \quad \quad -\quad 0064\quad \quad \downarrow \ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ 169)\quad \quad \quad 16\quad 00\ \quad \quad -\quad \quad \quad \quad 1529\ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \quad \ \quad \quad \quad \quad \quad \quad \quad \quad 71\quad \quad \quad \ Rounding\quad off\quad :\quad 0.089\ \ $

State true or false:

The square root of 5.2005 correct to two decimal places is 2.28.

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

  1. True

  2. False

Show answer
Correct Option: A
Explanation:

$\quad \ \quad \quad \quad \quad \quad 2.287\ \quad \quad \quad \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ \quad \quad 2)5.\quad 20\quad 05\ \quad \quad \quad -4\quad \downarrow \ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ 42)01\quad 20\ \quad \quad -0084\quad \quad \downarrow \ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ 448)\quad 036\quad 05\ \quad \quad -\quad \quad 3584\quad \quad \downarrow \ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ \quad \quad \quad \quad \quad \quad \quad 21\quad $

The square root of 245 correct to two places of decimal is 15.65
State true or false

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

  1. True

  2. False

Show answer
Correct Option: A
Explanation:

$\quad \ \quad \quad \quad \quad \quad 15.65\ \quad \quad \quad \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ \quad 15)245.00\quad 00\ \quad \quad -225\quad \downarrow \ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ 306)\quad 20\quad 00\ \quad \quad -1836\quad \quad \downarrow \ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ 3125)164\quad 00\ \quad \quad -\quad \quad 15625\ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \quad \ \quad \quad \quad \quad \quad \quad 845\quad \quad \ Rounding\quad off\quad :\quad 15.65\ \ $