Tag: approximation of square roots

Questions Related to approximation of square roots

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\ \ $

The square root of 0.065 correct to three places of decimal is 0.255
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 0.254\ \quad \quad \quad \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ \quad \quad 2)\quad 0.06\quad 50\quad 00\ \quad \quad \quad -0.04\quad \downarrow \ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ \quad 45)\quad \quad \quad 2\quad 50\ \quad \quad -\quad \quad 225\quad \quad \downarrow \ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ \quad 504)\quad \quad \quad 25\quad 00\ \quad \quad -\quad \quad \quad \quad 2016\ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \quad \ \quad \quad \quad \quad \quad \quad \quad \quad 484\quad \quad \quad \ \ $

The square root of 82.6 correct to two places of decimal is 9.09
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 9.087\ \quad \quad \quad \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ \quad \quad 9)82.60\quad 00\ \quad \quad \quad -81\quad \downarrow \ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ 180)\quad 01\quad 60\ \quad \quad -0000\quad \quad \downarrow \ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ 1808)\quad 160\quad 00\ \quad \quad -\quad \quad 12864\quad \quad \downarrow \ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \quad \ 19167)\quad \quad \quad \quad \quad 3136\quad 00\quad \ \quad \quad \quad \quad \quad \quad \quad \quad \quad -31129\quad \quad \downarrow \ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ \qquad \qquad \qquad \qquad 282471\quad $

State true or false.
The square root of 0.602 correct to two decimal places is 0.78.

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 0.77\ \quad \quad \quad \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ \quad \quad 7)\quad 0.60\quad 20\ \quad \quad \quad -0.49\quad \downarrow \ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ 147)\quad \quad 11\quad 20\ \quad \quad -\quad 1029\quad \quad \downarrow \ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ \quad \quad \quad \quad \quad 191\quad $

Find the square root of $\displaystyle 1 \frac{5}{16}$  correct to two decimal places

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

  1. $1.14$

  2. $1.15$

  3. $1.65$

  4. $1.12$

Show answer
Correct Option: B
Explanation:

 $\displaystyle 1 \dfrac{15}{16}$

$=\dfrac{21}{16}$
$=1.3125$

$1$$1$ $1.3125$$1$
$21$  $1$ $31$$21$
$224$   $4$ $1025$$896$
$2285$ $12900$$11425$                  $1475$

Therefore,
Square root of $\displaystyle 1 \frac{15}{16}=1.145$
                                   $=1.15$

Find the square root of $\displaystyle 6 \frac{7}{8}$ correct to two decimal places 

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

  1. $2.62$

  2. $2.61$

  3. $2.63$

  4. $2.6$

Show answer
Correct Option: A
Explanation:

 $\displaystyle 6 \frac{7}{8}$
$=\dfrac{55}{8}$
$=6.875$

$2$$2$ $6.875$$4$
$46$  $6$ $287$$276$
$522$    $1150$$1044$
$6$                  

Therefore,
Square root of $\displaystyle 6 \frac{7}{8}=2.62$