Tag: maths

Questions Related to maths

If the sum $S$ of three consecutive even numbers is a perfect square between $200\;and\;400$, then the square root of $S$ is

maths square root square root of perfect square finding square root of a number square root of a perfect square

  1. $15$

  2. $16$

  3. $18$

  4. $19$

Show answer
Correct Option: C
Explanation:

$15^2=225,\;16^2=256$
$17^2=281\;18^2=324$
$19^2=361$
$\;2x-2+2x+2x+2=6(x)$
$\Rightarrow6x=324$ is possible
$\Rightarrow\sqrt{324}=18$

Therefore,square root of $S$ is $18$

Find the length of the side of a square whose area is 441 $ \displaystyle m^{2} $.

maths square root square root of perfect square finding square root of a number square root of a perfect square

  1. $19 $ m

  2. $21 $ m

  3. $23 $ m

  4. $29 $ m

Show answer
Correct Option: B
Explanation:

Given the area of the square is $441\ m^2$ .

We know the area of the square is side$^{ 2 }$
So, the square root of side is $\sqrt { 441 } =\sqrt{3\times\ 3\times 7\times 7}=3\times 7=21$.
The side of the square is $21$ m.

Two square roots of the unity are

maths square root square root of perfect square finding square root of a number square root of a perfect square

  1. $1, -1$

  2. $-1, \omega$

  3. $1, -\omega$

  4. $i, i^2$

Show answer
Correct Option: A
Explanation:

Square root of unity is 1 and  -1 as $1^2={-1}^2=1$

Inverse operation of squares is known as:

maths square root square root of perfect square finding square root of a number square root of a perfect square

  1. minimum number

  2. square root

  3. odd number

  4. prime number

Show answer
Correct Option: B
Explanation:

To get inverse ( opposite operation) of squares. Division is opposite of Multiplication.

$13 \times 13 =169$ ( Square)

$169 \div 13 = 13$ ( Square root)

Therefore, B is the correct answer

$\sqrt{0.0169 \times ?}= 1.3$

maths square root square root of perfect square finding square root of a number square root of a perfect square

  1. 10

  2. 100

  3. 1000

  4. None of these

Show answer
Correct Option: B
Explanation:

Let $\sqrt{0.0169 \times x}=1.3$
Then,  $0.0169x = (1.3)^2 = 1.69$
$\Rightarrow x=\frac{1.69}{0.0169}=100$

Solve of simplify the following problem, using the properties of roots:
$\sqrt { 20a } \times \sqrt { 5a }$, assuming $a$ is positive

maths square root square root of perfect square finding square root of a number square root of a perfect square

  1. $10a$

  2. $12a$

  3. $15a$

  4. $5a$

Show answer
Correct Option: A
Explanation:

$10a: \sqrt { 20a } \times \sqrt { 5a } =\sqrt{100{a}^{2}}=10a$

State whether true or false:
$\cfrac{\sqrt{12}}{\sqrt{3}}$ is not a rational number as $\sqrt{12}$ and $\sqrt{3}$ are not integers. 
maths square root square root of perfect square finding square root of a number square root of a perfect square

  1. True

  2. False

Show answer
Correct Option: B
Explanation:

False

$\cfrac{\sqrt{12}}{\sqrt{3}}=\sqrt{4}=2$ which is a rational number.

Value of $\sqrt{10+\sqrt{25+\sqrt{121}}}$ in the following is 

maths square root square root of perfect square finding square root of a number square root of a perfect square

  1. 5

  2. 3

  3. 4

  4. 6

Show answer
Correct Option: C
Explanation:

$\sqrt{10+\sqrt{25+\sqrt{121}}}$
$=\sqrt{10+\sqrt{15+11}}$
$=\sqrt{10+6}=\sqrt{16}=4$

Square root of $400$ is?

maths square root square root of perfect square finding square root of a number square root of a perfect square

  1. $40$

  2. $25$

  3. $20$

  4. $100$

Show answer
Correct Option: C
Explanation:

$400=2\times 200$

       $=2\times 2\times 100$
       $=2\times 2\times 2\times 50$
       $=2\times 2\times 2\times 2\times 25$
       $=2\times 2\times 2\times 2\times 5\times 5$
       $=2^4\times 5^2$
$\Rightarrow$  $400=2^4\times 5^2$
$\Rightarrow$  $\sqrt{400}=\sqrt{2^4\times 5^2}$
$\Rightarrow$  $\sqrt{400}=2^2\times 5$
$\Rightarrow$  $\sqrt{400}=4\times 5$
$\Rightarrow$  $\sqrt{400}=20$

The value  of  $\sqrt {11 - \sqrt{112} }=  $

maths square root square root of perfect square finding square root of a number square root of a perfect square

  1. $2 + \sqrt{7}$

  2. $2 - \sqrt{7}$

  3. $ \sqrt{7} - 2$

  4. none of these

Show answer
Correct Option: C
Explanation:
$11-\sqrt {112}$

$=11-\sqrt {4\times 28}$

$=11-\sqrt {4}\times \sqrt {28}$

$=11-2\times \sqrt {28}$

$=11-2\times \sqrt {7}\times \sqrt {4}$

$=7+4-2\times \sqrt {7}\times \sqrt {4}$

$=(\sqrt {7})^2 +(\sqrt {4})^2 -2\times \sqrt {7}\times \sqrt {4}$

$=(\sqrt {7}-\sqrt {4})^2$

Thus, $11-\surd {112}=(\surd {7} -\surd {4})^2$

Hence,

$\sqrt {11-\sqrt {112}}=\sqrt {(\sqrt {7}-\sqrt {4})^2}=\sqrt {7}-\sqrt {4}=\sqrt {7}-2$