Tag: squares and square roots

Questions Related to squares and square roots

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 $\displaystyle 6 \frac{7}{8}=2.62$
                             

Consider the Following values of the three given number $\displaystyle \sqrt{103},$ $\displaystyle \sqrt{99.35},$ $\displaystyle \sqrt{102.20},$
1.10.1489 (approx,)
2.10.109(approx,)
3.9.967 (approx,)
The correct sequence of the these values matching with the above number is:

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

  1. 1, 2, 3

  2. 1, 3, 2

  3. 2, 3, 1

  4. 3, 1, 2

Show answer
Correct Option: B
Explanation:

$\sqrt{3}=10.14889$
$\sqrt{99.35}=9.967$
$\sqrt{102.30}=10.1094$
Hence,The correct sequence of the these values matching with the above number is:1,3,2

$\sqrt{1\, +\, \sqrt{1\, +\, \sqrt{1\, +\, ..........}}}\, =\, ..........$   

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

  1. Equals 1

  2. Lies between 0 and 1

  3. Lies between 1 and 2

  4. Is greater than 2

Show answer
Correct Option: C
Explanation:

Let 


$x=\sqrt{1+\sqrt{1-----}}$

Squaring both sides

$x^2=1+\sqrt{1+\sqrt{1+\sqrt{1------}}}$

$x^2=1+x$                $(\because x=\sqrt{1+\sqrt{1------}})$

$x^2-x-1=0$

finding roots, we get

$\dfrac{1\pm\sqrt{1+4}}{2}$

$=\dfrac{1\pm\sqrt{5}}{2}$

$=-0.615$ and $1.615$

If $x\, \ast\, y\, =\, \sqrt{x^2\, +\, y^2}$, then the value of $(1^{\ast}\, 2\, \sqrt{2})(1^{\ast}\, - 2\, \sqrt{2})$ is:  

maths squares and square roots approximation of square roots estimating square roots square root of non perfect squares
    • 7

  2. 0

  3. 2

  4. 9

Show answer
Correct Option: D
Explanation:

$1^{\ast} 2 \sqrt{2}\, =\, \sqrt{(1)^2\, +\, (2 \sqrt{2}^2}\, =\, \sqrt{1\, +\, 8}\, =\, 3$

$1^{\ast} -2 \sqrt{2}\, =\, \sqrt{(1)^2\, +\, (-2 \sqrt)^2}\, =\, \sqrt{1\, +\, 8}\, =\, 3$
$(1\, \ast\, 2 \sqrt{2})(1\, \ast\, -2 \sqrt{2})\, =\, (3)(3)\, =\, 9$

$\displaystyle \frac{\sqrt{32}\, +\, \sqrt{48}}{\sqrt{8}\, +\, \sqrt{12}}\, =\, ?$

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

  1. $\sqrt{2}$

  2. 2

  3. 4

  4. 8

Show answer
Correct Option: B
Explanation:
$ {\cfrac{\sqrt{32} + \sqrt{48}}{\sqrt{8} + \sqrt{12}} = \cfrac{\sqrt{16 \times 2} + \sqrt{16 \times 3}}{\sqrt{4 \times 2} + \sqrt{4 \times 3}}}$

$= \cfrac{4\sqrt{2} + 4\sqrt{3}}{2\sqrt{2} + 2\sqrt{3}}$

$ = \cfrac{4 \left (\sqrt{2} + \sqrt{3} \right )}{2 \left (\sqrt{2} + \sqrt{3} \right )}$

$ = 2$

If $\sqrt{2}\, =\, 1.4142,$ then the value of $\displaystyle \frac{2}{9}$ is

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

  1. 0.2321

  2. 0.4714

  3. 0.3174

  4. 0.4174

Show answer
Correct Option: B
Explanation:

$\displaystyle {\sqrt {\frac{2}{9}}\, =\, \frac{\sqrt{2}}{\sqrt{9}}\, =\, \frac{\sqrt{2}}{3}\, =\, \frac{1.4142}{3}\, =\, 0.4714.}$