Tag: squares and square roots

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Questions Related to squares and square roots

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

The square root of 0.065 correct to three places of decimal is 0.255
State true or false

  1. True

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

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

The square root of 82.6 correct to two places of decimal is 9.09
State true or false.

  1. True

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

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

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

  1. True

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

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

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

  1. $1.14$
  2. $1.15$
  3. $1.65$
  4. $1.12$
Reveal answer Fill a bubble to check yourself
B Correct answer
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 $\displaystyle 1 \frac{15}{16}=1.145$
                                   $=1.15$

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

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

  1. $2.62$
  2. $2.61$
  3. $2.63$
  4. $2.6$
Reveal answer Fill a bubble to check yourself
A Correct answer
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 $\displaystyle 6 \frac{7}{8}=2.62$
                             

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

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:

  1. 1, 2, 3

  2. 1, 3, 2

  3. 2, 3, 1

  4. 3, 1, 2
Reveal answer Fill a bubble to check yourself
B Correct answer
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

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

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

  1. Equals 1

  2. Lies between 0 and 1

  3. Lies between 1 and 2

  4. Is greater than 2
Reveal answer Fill a bubble to check yourself
C Correct answer
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 $1.615$

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

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

    • 7

  2. 0

  3. 2

  4. 9
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

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

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

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

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

  1. $\sqrt{2}$

  2. 2

  3. 4

  4. 8
Reveal answer Fill a bubble to check yourself
B Correct answer
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$