Tag: square and square root

Questions Related to square and square root

The value of $3x\sqrt{2y}$ is

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

  1. $\sqrt{18x^2y}$

  2. $\sqrt{6x^2y}$

  3. $\sqrt{12xy}$

  4. $\sqrt{18xy}$

Show answer
Correct Option: A
Explanation:

$3x\sqrt{2y}=\sqrt{2y\times3^2x^2}=\sqrt{18x^2y}$ 

Find the square of $59$

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

  1. $3481$

  2. $8151$

  3. $3451$

  4. $3145$

Show answer
Correct Option: A
Explanation:

$59^{2} = 59 \times 59 = 3481$

$13^2 = 169$, Is it true for only $13$?

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

  1. No

  2. Yes

  3. Incomplete

  4. Not sur

Show answer
Correct Option: A
Explanation:

It can also be $(-13)^2$

$-13 \times -13 = 169$

Therefore, A is the correct answer.

If $ \displaystyle (ab^{-1})^{2x-1}=(ba^{-1})^{x-2}  $ then what is the value of x?

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

  1. $-1$

  2. $2$

  3. $-3$

  4. $4$

Show answer
Correct Option: A
Explanation:
$(ab^{-1})^{2x-1}=(ba^{-1})^{x-2}$
$\Rightarrow \left ( \frac{1}{ab} \right )^{2x-1}=\left ( \frac{1}{ab} \right )^{x-2}$
$2x-1=x-2\Rightarrow x=-1$

Find the square of: $6.3$

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

  1. $39.69$

  2. $39.56$

  3. $39.60$

  4. $39.03$

Show answer
Correct Option: A
Explanation:

Square of $6.3 = 6.3\times 6.3=\dfrac {63}{10}\times \dfrac {63}{10}=\dfrac {3936}{100}$
                        $= 39.69$

Is $2352$ a perfect square ? If not, find the greater number closest to $2352$,  which is a perfect square. Find the square root of the new number.

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

  1. Yes, $2352$ a perfect square.

  2. No, $2352$  is not a perfect square else $2304$  is closest perfect square.
    Square root of $2304\ is\  48$

  3. No, $2352$  is not a perfect square else $2401$  is closest perfect square.
    Square root of $2401\ is\  49$

  4. Data insufficient

Show answer
Correct Option: C
Explanation:

We have 2352 =  $ \displaystyle \underline{2\times 2}\times \underline{2\times 2}\times 3\times \underline{7\times 7} $
As the prime factor 3 has no pair 2352 is not a perfect square 

Nearest no. bigger than  $2352$ and square is $2401 =49\times49$

If $\displaystyle { m }^{ -1 }=-\frac { 1 }{ 3 } $, then $\displaystyle { m }^{ -2 }$ is equal to

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

  1. $-9$

  2. $-3$

  3. $\cfrac{-1}{9}$

  4. $\dfrac{1}{9}$

  5. $9$

Show answer
Correct Option: D
Explanation:

$\dfrac{1}{m}$ $=$ $\dfrac{-1}{3}$

$m=-3$
$m^{2}$ $=$ $9$
$\dfrac{1}{m^2}$ $=$ $\dfrac{1}{9}$
Hence, Option D is correct.

Which number is added to the missing place of  $10000+2400+.......$ to form a square of  $112$?

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

  1. $100$

  2. $112$

  3. $113$

  4. $144$

Show answer
Correct Option: D
Explanation:

$112^2 = (100 + 12)^2$
$a = 100, b = 12$
$= a(a + b) + b(a + b)$
$= 100(100 + 12) + 12(100 + 12)$
$= 100^2 + 1200 + 1200 + 12^2$
$= 10000 + 2400 + 144$
$= 12544$
The missing number is 144.

$025$ is square of $55$.What digit should replace $$?

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

  1. $1$

  2. $2$

  3. $3$

  4. $4$

Show answer
Correct Option: C
Explanation:

Step 1: 

Multiply ten's digit with its next number.
$5 \times (5 + 1) = 5 \times 6 = 30 ---(1)$
Step 2:Find the square of unit's digit: 5
$5^2$ = 25 ----(2)
Step 3 :
Joining (1) and (2), we get
$3025 = 55 \times 55$
So, 3 is the missing number.

$25$ is a square of $25$. Which digit should replace $$?

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

  1. $3$

  2. $4$

  3. $5$

  4. $6$

Show answer
Correct Option: D
Explanation:

Step 1 :Multiply ten's digit with its next number.
$2 \times (2 + 1) = 2\times 3 = 6 ---(1)$
Step 2 : Find the square of unit's digit: 5
$5^2 = 25 ----(2)$
Combining (1) and (2), we get
$25 \times 25 = 625$
$6 $ is the missing number.