Tag: squares and square roots

Quizzes (7) Questions (116)

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

$\sqrt{2\sqrt{2\sqrt{2\sqrt{2\sqrt{2}}}}}\, =\, ?$

  1. 0

  2. 1

  3. 2
  4. $2^{31/32}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$\sqrt{2\, \times\, \sqrt{2\, \times\, \sqrt{2\, \times\, \sqrt{2\, \times\, 2^{1/2}}}}}$

$=\, \sqrt{2\, \times\, \sqrt{2\, \times\, \sqrt{(2\, \times\, 2^{3/4})}}}$
$=\, \sqrt{2\, \times\, \sqrt{2\, \times\, 2^{7/8}}}\, =\, \sqrt{2\, \times\, 2^{15/16}}\, =\, 2^{31/32}$

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

By using the table for square root find the value of
$13.21$
$21.97$

  1. 3.63, 4.60

  2. 3.63, 4.69

  3. 3.53, 4.69

  4. 3.63, 4.19
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

(i)

From square root table, Square root of 13.21 is:

 √13.21 = 3.6345

Therefore,

The square root of 13.21 is 3.63

(ii) From square root table, Square root of 21.97 is:

 √21.97 = 4.687

Therefore,

The square root of 21.97 is 4.69

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 $10$, correct to four places of decimal.

  1. 3.4623

  2. 3.1023

  3. 3.1693

  4. 3.1623
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
$3.16227$
$3$$+3$ $10$$9$
$61$$+1$ $100$$61$
$626$$+6$ $3900$$3756$
$6322$$+2$ $14400$$12644$
$63242$$+2$-------------$632447$ $175600$$126484$---------------$4911600$$4427129$

$\sqrt{10}=3.16227\simeq 3.1623$
$\therefore$ The square root of $10$ correct to four places of decimal is $3.1623$

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

The square root of $\displaystyle \frac{\left ( 3\frac{1}{4} \right )^{4}-\left ( 4\frac{1}{3} \right )^{4}}{\left ( 3\frac{1}{4} \right )^{2}-\left ( 4\frac{1}{3} \right )^{2}}$ is

  1. $\displaystyle 7\frac{5}{12}$
  2. $\displaystyle 7\frac{7}{12}$
  3. $\displaystyle 5\frac{5}{12}$
  4. $\displaystyle 5\frac{7}{12}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$\frac{\left ( 3\tfrac{1}{4} \right )^{4}-\left ( 4\tfrac{1}{3} \right )^{4}}{\left ( 3\tfrac{1}{4} \right )^{2}-\left ( 4\tfrac{1}{3} \right )^{2}}$

=$\frac{\left [ \left ( 3\tfrac{1}{4} \right )^{2}+\left ( 4\tfrac{1}{3} \right )^{2} \right ]\left [ \left ( 3\tfrac{1}{4} \right )^{2}-\left ( 4\tfrac{1}{3} \right )^{2} \right ]}{\left ( 3\tfrac{1}{4} \right )^{2}-\left ( 4\tfrac{1}{3} \right )^{2}}$
=$\left ( 3\tfrac{1}{4} \right )^{2}+\left ( 4\tfrac{1}{3} \right )^{2}$
=$\left ( \frac{13}{16} \right )^{2}+\left ( \frac{13}{9} \right )^{2}=169\times \left ( \frac{9+16}{144} \right )=169\times\frac{25}{144}$ 
Then squire root =$\frac{13\times 5}{12}=\frac{65}{12}$=$5\frac{5}{12}$

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.