Tag: square root

Questions Related to square root

Simplify the expression involving rational exponents:
${ \left( \displaystyle\frac { 25 }{ 64 }  \right)  }^{ { 1 }/{ 2 } }$

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

  1. $\displaystyle\frac { 25 }{ 8 } $

  2. Not a real number

  3. $\displaystyle\frac { 5 }{ 8 } $

  4. $\displaystyle\frac { 5 }{ 64 } $

Show answer
Correct Option: C
Explanation:

$\left(\dfrac{25}{64}\right)^\frac{1}{2}$ = $\left(\dfrac{5^2}{8^2}\right)^\frac{1}{2}$ = $\dfrac{5}{8}$

If $n = \sqrt {\dfrac {16}{81}}$, what is the value of $\sqrt {n}$?

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

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

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

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

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

  5. $\dfrac {9}{2}$

Show answer
Correct Option: D
Explanation:

Since $n = \sqrt {\dfrac {16}{81}} = \dfrac {4}{9}$, 
then $\sqrt {n} = \sqrt {\dfrac {4}{9}} = \dfrac {2}{3}$.

The correct answer is D.

Find the square root of decimal 5.76.

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

  1. $4.2$

  2. $2.4$

  3. $18.4$

  4. $4.23$

Show answer
Correct Option: B
Explanation:

$576=2^{6} \times 3^{6}=(2^{3} \times3)^2=(24)^{2}$

$100=2^{2} \times 5^{2}=(2 \times5)^{2}=(10)^{2}$
$\sqrt{5.76}=\sqrt{\dfrac{576}{100}}$=$\sqrt{({\dfrac{24}{10}})^{2}}$
$=\dfrac{24}{10}=2.4$

The square root of $144$ is 

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

  1. $114$

  2. $442$

  3. $12$

  4. $24$

Show answer
Correct Option: C
Explanation:

$144 = 2\times2\times2\times2\times 3\times3$

$\sqrt{144} = \sqrt{2\times2\times2\times2\times 3\times3}=2\times2\times3=12$

Find the square root of $81$.

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

  1. $9$

  2. $45$

  3. $18$

  4. $81$

Show answer
Correct Option: A
Explanation:

$ 81 = 3\times3\times3\times3$

$\sqrt{ 81} = \sqrt{3\times3\times3\times3}=3\times3=9$

Complete the repeated subtraction to find the square root of $225$.

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

  1. $9$

  2. $45$

  3. $25$

  4. $15$

Show answer
Correct Option: D
Explanation:

$225 -1 = 224$ ,

$224 -3 = 221 $,
$221-  5 = 216$, 
$216 -7 = 209$,
$209 - 9= 200$ ,
$200 -11 = 189$
$189-  13 = 176$ , 
$176-  15 = 161$, 
$161 -17 = 144$,
$144- 19 = 125$
$125 - 21 = 104 $
$ 104-  23 = 81 $
$81-  25 = 56$
$ 56-  27 = 29$, 
$29 -29 = 0 = 15$ 
Therefore, D is the correct answer.

Simplify the following : $\sqrt { 0.0081 } $

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

  1. $0.02$

  2. $0.09$

  3. $0.06$

  4. $0.05$

Show answer
Correct Option: B
Explanation:
$0.09$: Since $(0.09)(0.09)=0.0081$, 

$\sqrt{0.0081}=0.09$. 

You can also rewrite $0.0081$ as $81\times {10}^{-4}$

$\sqrt { 81\times { 10 }^{ -4 } } =\sqrt { 81 } \times \sqrt { { 10 }^{ -4 } } =9\times { \left( { 10 }^{ -4 } \right)  }^{ \frac { 1 }{ 2 }  }=9\times { 10 }^{ -2 }=0.09$

Which of the following is the value of $\displaystyle \sqrt { \sqrt [ 3 ]{ 0.000064 }  } $ ?

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

  1. $0.004$

  2. $0.008$

  3. $0.02$

  4. $0.04$

  5. $0.2$

Show answer
Correct Option: E
Explanation:

$\sqrt[3]{0.000064}$$=$$0.04$

$\sqrt{0.04}$$=$$0.2$
 $\therefore \displaystyle \sqrt { \sqrt [ 3 ]{ 0.000064 }  } =0.2$
Hence, Option E is correct.

What is the value of $\sqrt{\frac{400}{25}}$?

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

  1. 4

  2. 3

  3. 2

  4. 1

Show answer
Correct Option: A
Explanation:

$\sqrt{\dfrac{400}{25}}$
= $\dfrac{20}{5} = 4$.

Find the value of $\sqrt{\frac{484}{121}}$

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

  1. 4

  2. 3

  3. 2

  4. 1

Show answer
Correct Option: C
Explanation:

$\sqrt{\dfrac{484}{121}}$
= $\dfrac{22}{11}$
= 2