Tag: square and square root

Questions Related to square and square root

$(\cfrac{9 \times 12}{4\times 3})^2$ = ?

maths square and square root perfect square or square number squares and triangles powers and roots

  1. $80$

  2. $76$

  3. $91$

  4. $81$

Show answer
Correct Option: D
Explanation:

$(\cfrac{9 \times 12}{4\times 3})^2 = (\cfrac{81 \times 144}{16\times 9})$ 
On simplifying, we get
$(\cfrac{9 \times 12}{4\times 3})^2 = 81$

$(\dfrac{24}{4\times 12})^2$ = ?

maths square and square root perfect square or square number squares and triangles powers and roots

  1. $\dfrac{3}{4}$

  2. $\dfrac{1}{4}$

  3. $\dfrac{5}{4}$

  4. $\dfrac{1}{3}$

Show answer
Correct Option: B
Explanation:

$4\times12$ $=$ $48$

$(\dfrac{24}{48})^2$=$(\dfrac{1}{2})^2$ 
$=$ $\dfrac{1}{4}$
Hence, Option B is correct.

$(\dfrac{30 \times 25}{60\times 5})^2$ = ?

maths square and square root perfect square or square number squares and triangles powers and roots

  1. $\dfrac{15}{4}$

  2. $\dfrac{25}{3}$

  3. $\dfrac{12}{4}$

  4. $\dfrac{25}{4}$

Show answer
Correct Option: D
Explanation:

$30\times25$ $=$ $750$

$60\times5$ $=$ $300$
$\dfrac{750}{300}$ $=$ $\dfrac{5}{2}$
$\dfrac{5}{2}$$\times$$\dfrac{5}{2}$ $=$ $\dfrac{25}{4}$
Hence, Option D is correct.

If a four-digit perfect square number is such that the number formed by the first two digits and the number formed by the last two digits are also perfect squares, identify the four digit number.

maths square and square root perfect square or square number squares and triangles powers and roots

  1. $6416$

  2. $3616$

  3. $1681$

  4. $1664$

Show answer
Correct Option: C
Explanation:

Four digit number $accd$

$ab$ is a perfect square
$cd$ is also a perfect square
Consider $6416$
$64$and$16$ are perfect square but $6416$ is not a perfect square.
Consider $3616$
$36$and$16$ are perfect square but $3616$ is not a perfect square.

Consider $1681$
$16$and$81$ are perfect square and $1681$ is a perfect square.

Consider $1664$
$16$and$64$ are perfect square but $1664$ is not a perfect square.
Hence, Option C is correct.


Determine the square for the rational number: $(\dfrac{16\times24}{48})$

maths square and square root perfect square or square number squares and triangles powers and roots

  1. $64$

  2. $16$

  3. $46$

  4. $48$

Show answer
Correct Option: A
Explanation:

$(\cfrac{16\times24}{48})^2$
On simplifying, we get

$(\cfrac{24}{3})^2$
$ = 8^2$
$= 64$

Determine the square for the rational number: $(\cfrac{5\times25}{50})$

maths square and square root perfect square or square number squares and triangles powers and roots

  1. $\dfrac{5}{2}$

  2. $\dfrac{4}{25}$

  3. $\dfrac{5}{4}$

  4. $\dfrac{25}{4}$

Show answer
Correct Option: D
Explanation:

$(\cfrac{5\times25}{50})^2$
On simplifying, we get
$(\cfrac{5\times25}{50})^2 = (\cfrac{5}{2})^2$
= $\cfrac{25}{4}$

Evaluate the product of $2.3\times 10^4$ and $3\times 10^3$.

maths square and square root scientific notation use of exponents power of 10

  1. $6.9\times 10^4$

  2. $6.9\times 10^7$

  3. $6.9\times 10^8$

  4. $6.9\times 10^6$

Show answer
Correct Option: B
Explanation:

$(2.3\times 10^4) \times (3 \times 10^3)$
$\Rightarrow (2.3 \times 3) \times(10^{3+4})$

$\therefore 6.9 \times 10^7$
Ans- Option $B$.

Evaluate $\dfrac{6.3\times 10^3}{3\times 10^7}$

maths square and square root scientific notation use of exponents power of 10

  1. $2\times 10^{-3}$

  2. $2.1\times 10^{-3}$

  3. $2.1\times 10^{-4}$

  4. $2\times 10^{-5}$

Show answer
Correct Option: C
Explanation:

$\dfrac{6.3\times 10^{3}}{3\times 10^7}$


$\Rightarrow \dfrac{6.3}{3} \times 10^{3-7}$


$\therefore 2.1\times 10^{-4}$

Ans-Option $C$.

Solve:

$\cfrac{2.3^{n+1} + 7.3^{n-1}}{3^{n+2}-2 \left ( \cfrac{1}{3} \right )^{1-n}} $

maths square and square root scientific notation use of exponents power of 10

  1. $0$

  2. $1$

  3. $2$

  4. $3$

Show answer
Correct Option: B
Explanation:

We have,

$\cfrac{2.3^{n+1} + 7.3^{n-1}}{3^{n+2}-2 \left ( \cfrac{1}{3} \right )^{1-n}}  $

$\Rightarrow \cfrac{6.3^n+ \dfrac{7}{3}.3^n}{9.3^n-\dfrac{2}{3}. 3^n}  $

$\Rightarrow \cfrac{18.3^n+ 7.3^n}{27.3^n-2. 3^n}  $

$\Rightarrow \cfrac{25.3^n}{25.3^n}  $

$\Rightarrow 1  $

Hence, this is the answer.

The average distance between the Sun and a certain planet is approximately $\displaystyle 2.3\times { 10 }^{ 14 }$ inches. Which of the following is closest to the average distance between the Sun and the planet, in kilometers? (1 kilometer is approximately $\displaystyle 3.9\times { 10 }^{ 4 }$ inches )

maths square and square root scientific notation use of exponents power of 10

  1. $\displaystyle 7.1\times { 10 }^{ 8 }$

  2. $\displaystyle 5.9\times { 10 }^{ 9 }$

  3. $\displaystyle 1.6\times { 10 }^{ 10 }$

  4. $\displaystyle 1.6\times { 10 }^{ 111 }$

  5. $\displaystyle 5.9\times { 10 }^{ 11 }$

Show answer
Correct Option: B
Explanation:

The average distance in KM will be $\frac { 2.3\times { 10 }^{ 14 } }{ 3.9\times { 10 }^{ 4 } } =0.59\times { 10 }^{ 10 }=5.9\times { 10 }^{ 9 }\quad km$

So correct answer will be option B