Tag: maths

Questions Related to maths

Find the squares of the following numbers without actual multiplication:
$49$
$52$

maths squares and square roots finding the square of a number finding square of a number patterns in square numbers

  1. $2441; 2704$

  2. $2401; 2784$

  3. $2401; 2704$

  4. $2441; 2784$

Show answer
Correct Option: C
Explanation:

$49^2=(40+9)^2=40(40+9)+9(40+9)$
$\;\;\;\;\;=(40)^2+40\times9+9\times40+9^2$
$\;\;\;\;\;=1600+360+360+81$
So, $49^2=2401$
$52^2=(50+2)^2=50(50+2)+2(50+2)$
$\;\;\;\;\;\;=50^2+50\times2+2\times50+2^2$
$\;\;\;\;\;\;=2500+100+100+4$
So, $52^2=2704$.

Find the square of $43$ without multiplication.

maths squares and square roots finding the square of a number finding square of a number patterns in square numbers

  1. $2401$

  2. $4801$

  3. $1842$

  4. $1849$

Show answer
Correct Option: D
Explanation:

It can be written as $43 = 40+3$
$43^2= (40+3)^2  =40^2+2\times40\times3+3^2$
$= 1600+2\times 120+  9$
$= 1849$
Therefore, D is the correct answer.

Find the square of $125$.

maths squares and square roots finding the square of a number finding square of a number patterns in square numbers

  1. $84113$

  2. $48000$

  3. $15625$

  4. $84920$

Show answer
Correct Option: C
Explanation:

The square of $125^2$

$ = (120+5)^2$

$=14400+25+1200$

$=15625$     .....($(a+b)^2=(a^2+b^2+2ab))$

Without doing multiplication, find the square of $29.$

maths squares and square roots finding the square of a number finding square of a number patterns in square numbers

  1. $841$

  2. $480$

  3. $742$

  4. $849$

Show answer
Correct Option: A
Explanation:

It can be written as $29 = 20+9$

On squaring both sides, we get

$29^2=(20+9)^2$

$= 20^2+2\times20\times9+9^2$

$= 400+2\times 180+  81$

$= 841$

Therefore, option A is the correct answer.

Without actual finding the square of the numbers, find the value of $120^2 - 119^2$.

maths squares and square roots finding the square of a number finding square of a number patterns in square numbers

  1. $239$

  2. $240$

  3. $238$

  4. $237$

Show answer
Correct Option: A
Explanation:

Using the formula, $a^2 - b^2 = (a + b)(a - b)$
We get, $120^2 - 119^2 = (120 + 119)(120 - 119)$
$= 239 \times 1$
$= 239$.

Without actual finding the square of the numbers, find the value of $36^2 - 35^2$.

maths squares and square roots finding the square of a number finding square of a number patterns in square numbers

  1. $70$

  2. $71$

  3. $72$

  4. $73$

Show answer
Correct Option: B
Explanation:

Using the formula, $a^2 - b^2 = (a + b)(a - b)$
We get, $36^2 - 35^2 = (36 + 35)(36 - 35)$
$= 71 \times 1$
$= 71$.

Evaluate the following
$(0.98)^{2}$

maths squares and square roots finding the square of a number finding square of a number patterns in square numbers

  1. $0.9664$

  2. $0.9604$

  3. $0.9864$

  4. $0.9964$

Show answer
Correct Option: B
Explanation:

The given square $(0.98)^2$ can be evaluated as shown below:


${ (0.98) }^{ 2 }\ =(1-0.02)^{ 2 }\ =1^{ 2 }+(0.02)^{ 2 }-(2\times 1\times 0.02)\quad \quad \quad \quad \quad (\because \quad (a-b)^{ 2 }=a^{ 2 }+b^{ 2 }-2ab)\ =1+0.0004-0.04\ =1.0004-0.04\ =0.9604$

Hence, ${ (0.98) }^{ 2 }=0.9604$

A factor of $(3x^{4} - 12y^{4})$ is _________.

maths squares and square roots finding the square of a number finding square of a number patterns in square numbers

  1. $3$

  2. $x^{2} - 2y^{2}$

  3. $x^{2} + 2y^{2}$

  4. All of these

Show answer
Correct Option: A
Explanation:
Given expression is $(3x^{4}-12y^{4})$
Taking $3$ common, we get
$= 3(x^{4}-4y^{4})$
$= 3(x^4-(\sqrt{2}y)^{4})$
We know the identity and applying it $a^{2}-b^{2} = (a-b)(a+b)$

$3x^{4}-12y^{4}= 3(x^{4}-(\sqrt{2}y)^{4})$

$3x^{2}-12y^{2}= 3(x^{2}-\sqrt{2}y^{2})(x^{2}+\sqrt{2}y^{2})$

Find the square of the following number without multiplication.

46

maths squares and square roots finding the square of a number finding square of a number patterns in square numbers

  1. 2116

  2. 2002

  3. 2424

  4. 1988

Show answer
Correct Option: A
Explanation:

${46}^{2} = 46\times46 = 2116$

If sin$\theta -cosec  \theta =\sqrt{5},$ then the value of sin  $\theta  + cosec  \theta$ is:

maths squares and square roots finding the square of a number finding square of a number patterns in square numbers

  1. $\sqrt{3}$

  2. 1

  3. 3

  4. 9

Show answer
Correct Option: C
Explanation:

$\Rightarrow \sin\theta-cosec\theta=\sqrt{5}$


$\Rightarrow \sin\theta-\dfrac{1}{\sin\theta}=\sqrt{5}$      $(\because cosec\theta=\dfrac{1}{\sin\theta})$

$\Rightarrow \sin^2\theta-\sqrt{5}\sin\theta-1=0$

Solving equation to get roots.

$\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{\pm3+\sqrt{5}}{2}$ (substitute values to get roots)

To find:-

$\sin\theta+cosec\theta$

Using $\dfrac{3+\sqrt{5}}{2}$

$=\dfrac{3+\sqrt{5}}{2}+\dfrac{2}{3+\sqrt{5}}$

$=\dfrac{(3+\sqrt{5})^2+4}{2(3+\sqrt{5})}$

$=\dfrac{9+4+5+6\sqrt{5}}{2(3+\sqrt{5})}$

$=\dfrac{6(3+\sqrt{5})}{2(3+\sqrt{5})}$

$=3$


Using $\dfrac{-3+\sqrt{5}}{2}$

$=\dfrac{-3+\sqrt{5}}{2}+\dfrac{2}{-3+\sqrt{5}}$

$=\dfrac{(-3+\sqrt{5})^2+4}{2(-3+\sqrt{5})}$

$=\dfrac{9+4+5-6\sqrt{5}}{2(-3+\sqrt{5})}$

$=\dfrac{-6(-3+\sqrt{5})}{2(-3+\sqrt{5})}$

$=-3$


According to option answer is $3$